SQL Server 2012 AlwaysOn: need to automatically add databases by script- T-sql or PowerShell

Lots and lots of caveats here. I've tested this in a very limited way in a scenario where the data/log paths are congruent across all replicas, haven't added error handling, etc. You can call this stored procedure from the DDL trigger if you decide to go that way, as Kin suggested, or from a job, or what have you.

See additional comments inline.

CREATE PROCEDURE dbo.AddNewDBsToGroup
  @group SYSNAME = N'your_group_name', -- *** SPECIFY YOUR GROUP NAME HERE ***
  @path  SYSNAME = N'\\atel-web-be2\backups\',
  @debug BIT = 1
AS
BEGIN
  SET NOCOUNT ON;

  DECLARE 
    @sql        NVARCHAR(MAX) = N'',
    @remote_sql NVARCHAR(MAX) = N'';

  DECLARE @t TABLE(db SYSNAME);

  INSERT @t SELECT name FROM sys.databases 
  WHERE replica_id IS NULL AND database_id > 4;

  DECLARE @r TABLE(s NVARCHAR(512));

  -- get the *healthy* replicas available for this group
  -- you'll need error handling to handle cases where any
  -- of the replicas is currently *not* healthy. This 
  -- script does not tell you this happened.

  INSERT @r SELECT r.replica_server_name
  FROM sys.availability_groups AS g
  INNER JOIN sys.dm_hadr_availability_group_states AS s
  ON g.group_id = s.group_id
  INNER JOIN sys.availability_replicas AS r
  ON g.group_id = r.group_id
  AND r.replica_server_name <> @@SERVERNAME
  WHERE g.name = @group
  AND s.primary_replica = @@SERVERNAME
  AND s.primary_recovery_health_desc = 'ONLINE'
  AND s.synchronization_health_desc = 'HEALTHY';

  -- add the database to the group on the primary:

  SELECT @sql += N'ALTER AVAILABILITY GROUP ' 
    + QUOTENAME(@group) + ' ADD DATABASE ' + QUOTENAME(db) + ';'
  FROM @t;

  IF @debug = 1
  BEGIN
    PRINT @sql;
  END
  ELSE
  BEGIN
    EXEC master..sp_executesql @sql;
  END

  -- back up the database locally:
  -- this assumes your database names don't have characters illegal for paths

  SET @sql = N'';

  SELECT @sql += N'BACKUP DATABASE ' + QUOTENAME(db) -- ** BACKUP HAPPENS HERE **
    + ' TO DISK = ''' + @path + db + '.BAK'' WITH COPY_ONLY, FORMAT, INIT, COMPRESSION;
    BACKUP LOG ' + QUOTENAME(db) +
    ' TO DISK = ''' + @path + db + '.TRN'' WITH INIT, COMPRESSION;'
  FROM @t;

  IF @debug = 1
  BEGIN
    PRINT @sql;
  END
  ELSE
  BEGIN
    EXEC master..sp_executesql @sql;
  END

  -- restore the database remotely:
  -- this assumes linked servers match replica names, security works, etc.
  -- it also assumes that each replica has the exact sime data/log paths
  -- (in other words, your restore doesn't need WITH MOVE)

  SET @sql = N'';

  SELECT @sql += N'RESTORE DATABASE ' + QUOTENAME(db) -- ** RESTORE HAPPENS HERE **
    + ' FROM DISK = ''' + @path + db + '.BAK'' WITH REPLACE, NORECOVERY;
    RESTORE LOG ''' + @path + db + '.TRN'' WITH NORECOVERY;
    ALTER DATABASE ' + QUOTENAME(db) + ' SET HADR AVAILABILITY GROUP = '
    + QUOTENAME(@group) + ';'
  FROM @t; 

  SET @remote_sql = N'';

  SELECT @remote_sql += N'EXEC ' + QUOTENAME(s) + '.master..sp_executesql @sql;'
    FROM @r;

  IF @debug = 1
  BEGIN
    PRINT @sql;
    PRINT @remote_sql;
  END
  ELSE
  BEGIN
    EXEC sp_executesql @remote_sql, N'@sql NVARCHAR(MAX)', N'SELECT @@SERVERNAME;';
  END
END
GO

Once you've created the stored procedure, you can call it this way and look at the messages pane to see if it has identified the right group, databases, and servers before ever running it:

EXEC dbo.AddNewDBsToGroup @debug = 1;

When you are confident it is going to do the right thing (and you fully understand what 'the right thing" is), then change that to:

EXEC dbo.AddNewDBsToGroup @debug = 0;

If it fails, don't worry, it will tell you.

You don't have to write a cursor tsql script to check for new database created and schedule it to run for e.g. every minute. Instead use EVENTDATA() function in conjunction with server level trigger.

IF EXISTS (SELECT * FROM sys.server_triggers
    WHERE name = 'ddl_trig_database')
DROP TRIGGER ddl_trig_database
ON ALL SERVER;
GO
CREATE TRIGGER ddl_trig_database 
ON ALL SERVER 
FOR CREATE_DATABASE 
AS 
    PRINT 'Database Created.'
    SELECT EVENTDATA().value('(/EVENT_INSTANCE/TSQLCommand/CommandText)[1]','nvarchar(max)')
GO
DROP TRIGGER ddl_trig_database
ON ALL SERVER;
GO

Since you now have an automated mechanism in place that will fire up when a new database is created, you can use ALTER AVAILABILITY GROUP and ALTER DATABASE - SET HADR

basically you have to just include :

-- Move each database into the Availability Group
-- Change database name and Group as per your environment.
ALTER DATABASE Test1 SET HADR AVAILABILITY GROUP = TestAG
ALTER DATABASE Test2 SET HADR AVAILABILITY GROUP = TestAG
GO

Thinking of this a little bit more, you can be more creative to automate it --

-- create a driver table
create table AlwaysON_Candidates (
    DatabaseName sysname
    ,createdate datetime default getdate()
    ,IsAlwaysOnMember bit default 0 -- 0 = Not a part of AG
    ) -- 1 = Is part of AG
go
-- below insert will be governed by the server level trigger
insert into AlwaysON_Candidates (DatabaseName)
values ('Test1')
--- check the values in the driver table
select *
from AlwaysON_Candidates
--- add database to AG
alter database Test1
set HADR AVAILABILITY group = TestAG
-- update the bit in the driver table AlwaysON_Candidates
update AlwaysON_Candidates
set IsAlwaysOnMember = 1
where DatabaseName = 'Test1'

some good references for setting it up using tsql can be found here and here

EDIT: Below script will help you. Obviously you have to Understand it and test it in a test environment.

/************************************************************************************
Author  : Kin Shah
Version : 1.0.0 for dba.stackexchange.com

Note:   This script does not have ERROR handling and is not tested.
        Use at your own risk, It will print out the sql statements, but wont execute it
        unless the print statements have been modified to use "exec"

        UNDERSTAND the script and then test it on a TEST environment !!!!!!!!

*************************************************************************************/
-- create table 
set ansi_nulls on
go

set quoted_identifier on
go

create table AlwaysON_Candidates (
    ID int identity(1, 1)
    ,EventType nvarchar(128) null
    ,DatabaseName nvarchar(128) null
    ,LoginName nvarchar(128) null
    ,UserName nvarchar(128) null
    ,AuditDateTime datetime null
    ,IsAlwaysOnMember bit default 0
    )
go

alter table [dbo].[AlwaysON_Candidates] add default((0))
for [IsAlwaysOnMember]
go

-- create server trigger
if exists (
        select *
        from master.sys.server_triggers
        where parent_class_desc = 'SERVER'
            and name = N'ddl_trig_database'
        )
    drop trigger [ddl_trig_database] on all server
go

set ansi_nulls on
go

set quoted_identifier on
go

create trigger [ddl_trig_database] on all server
for CREATE_DATABASE as

insert into NewDatabases
select EVENTDATA().value('(/EVENT_INSTANCE/EventType)[1]', 'nvarchar(128)') as EventType
    ,EVENTDATA().value('(/EVENT_INSTANCE/DatabaseName)[1]', 'nvarchar(128)') as DatabaseName
    ,EVENTDATA().value('(/EVENT_INSTANCE/LoginName)[1]', 'nvarchar(128)') as LoginName
    ,EVENTDATA().value('(/EVENT_INSTANCE/UserName)[1]', 'nvarchar(128)') as UserName
    ,GETDATE() as AuditDateTime
    ,0 as IsAlwaysOnMember
go

set ansi_nulls off
go

set quoted_identifier off
go

ENABLE trigger [ddl_trig_database] on all server
go

--- PREREQUISITE ... CREATE A LINKED SERVER FROM PRIMARY TO SECONDARY SERVER !!!
--- fill in *** CHANGE HERE values 
--- test it on a TEST server
--- Not tested and not responsible for any dataloss. UNDERSTAND it and test it before implementing it.
declare @databasename varchar(max)
declare @sqlbackup varchar(max)
declare @sqlrestore varchar(max)
declare @PrimaryAG varchar(max)
declare @SecondaryAG varchar(max)
declare @backupPath varchar(max)

set @backupPath = '\\servername\sharedfolder\' --- *** CHANGE HERE

declare @group sysname

set @group = N'your_group_name' --- *** CHANGE HERE

declare @remotesql1 varchar(max)
declare @remotesql2 varchar(max)
declare @linkedserverName sysname

set @linkedserverName = 'kin_test_AG_LS' --- *** CHANGE HERE

select @databasename = min(DatabaseName)
from AlwaysON_Candidates
where IsAlwaysOnMember = 0

while @databasename is not null
begin
    -- ** BACKUP HAPPENS HERE **
    select @sqlbackup = N'BACKUP DATABASE ' + QUOTENAME(@databasename) + ' TO DISK = ''' + @backupPath + @databasename + '_forAG.BAK'' WITH COPY_ONLY, FORMAT, INIT, COMPRESSION;
    BACKUP LOG ' + QUOTENAME(@databasename) + ' TO DISK = ''' + @backupPath + @databasename + '_forAG.TRN'' WITH INIT, COMPRESSION;'
    from AlwaysON_Candidates
    where IsAlwaysOnMember = 0

    print @sqlbackup --- *** CHANGE HERE for EXEC master..sp_executesql @sqltext

    -- ** RESTORE HAPPENS HERE **
    select @sqlrestore = N'RESTORE DATABASE ' + QUOTENAME(@databasename) + ' FROM DISK = ''' + @backupPath + @databasename + '_forAG.BAK'' WITH REPLACE, NORECOVERY;
    RESTORE LOG ''' + @backupPath + @databasename + '_forAG.TRN'' WITH NORECOVERY;'

    print @sqlrestore

    select @remotesql1 = N'EXEC ' + QUOTENAME(@linkedserverName) + '.master..sp_executesql @sqlrestore;'

    print @remotesql1 --- *** CHANGE HERE for EXEC master..sp_executesql @sqltext

    -- join the AG group on primary
    select @PrimaryAG = N'ALTER AVAILABILITY GROUP ' + QUOTENAME(@group) + ' ADD DATABASE ' + QUOTENAME(@databasename) + ';'

    print @PrimaryAG --- *** CHANGE HERE for EXEC master..sp_executesql @sqltext

    -- join the AG group on secondary
    select @SecondaryAG = 'ALTER DATABASE ' + QUOTENAME(@databasename) + ' SET HADR AVAILABILITY GROUP = ' + QUOTENAME(@group) + ' ;'

    print @SecondaryAG

    select @remotesql2 = N'EXEC ' + QUOTENAME(@linkedserverName) + '.master..sp_executesql @sqlrestore;'

    print @remotesql2 --- *** CHANGE HERE for EXEC master..sp_executesql @SecondaryAG

    -- finally update the table 
    update AlwaysON_Candidates
    set IsAlwaysOnMember = 1
    where DatabaseName = @databasename

    -- go to another database if it is added newly
    select @databasename = min(DatabaseName)
    from AlwaysON_Candidates
    where IsAlwaysOnMember = 0
        and DatabaseName > @databasename
end