Use PHP composer to clone git repo

That package in fact is available through packagist. You don't need a custom repository definition in this case. Just make sure you add a require (which is always needed) with a matching version constraint.

In general, if a package is available on packagist, do not add a VCS repo. It will just slow things down.

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For packages that are not available via packagist, use a VCS (or git) repository, as shown in your question. When you do, make sure that:

• The "repositories" field is specified in the root composer.json (it's a root-only field, repository definitions from required packages are ignored)
• The repositories definition points to a valid VCS repo
• If the type is "git" instead of "vcs" (as in your question), make sure it is in fact a git repo
• You have a require for the package in question
• The constraint in the require matches the versions provided by the VCS repo. You can use composer show <packagename> to find the available versions. In this case ~2.3 would be a good option.
• The name in the require matches the name in the remote composer.json. In this case, it is gedmo/doctrine-extensions.

Here is a sample composer.json that installs the same package via a VCS repo:

{
    "repositories": [
        {
            "url": "https://github.com/l3pp4rd/DoctrineExtensions.git",
            "type": "git"
        }
    ],
    "require": {
        "gedmo/doctrine-extensions": "~2.3"
    }
}

The VCS repo docs explain all of this quite well.

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If there is a git (or other VCS) repository with a composer.json available, do not use a "package" repo. Package repos require you to provide all of the metadata in the definition and will completely ignore any composer.json present in the provided dist and source. They also have additional limitations, such as not allowing for proper updates in most cases.

Avoid package repos (see also the docs).

At the time of writing in 2013, this was one way to do it. Composer has added support for better ways: See @igorw 's answer

DO YOU HAVE A REPOSITORY?

Git, Mercurial and SVN is supported by Composer.

DO YOU HAVE WRITE ACCESS TO THE REPOSITORY?

Yes?

DOES THE REPOSITORY HAVE A composer.json FILE

If you have a repository you can write to: Add a composer.json file, or fix the existing one, and DON'T use the solution below.

Go to @igorw 's answer

ONLY USE THIS IF YOU DON'T HAVE A REPOSITORY
OR IF THE REPOSITORY DOES NOT HAVE A composer.json AND YOU CANNOT ADD IT

This will override everything that Composer may be able to read from the original repository's composer.json, including the dependencies of the package and the autoloading.

Using the package type will transfer the burden of correctly defining everything onto you. The easier way is to have a composer.json file in the repository, and just use it.

This solution really only is for the rare cases where you have an abandoned ZIP download that you cannot alter, or a repository you can only read, but it isn't maintained anymore.

"repositories": [
    {
        "type":"package",
        "package": {
          "name": "l3pp4rd/doctrine-extensions",
          "version":"master",
          "source": {
              "url": "https://github.com/l3pp4rd/DoctrineExtensions.git",
              "type": "git",
              "reference":"master"
            }
        }
    }
],
"require": {
    "l3pp4rd/doctrine-extensions": "master"
}