Generate ordered combinations with repetition

Python 2, 56 bytes

n is the maximum length and s is expected to be a list of characters. It is not clear to me whether n = 0 or an empty character list are valid inputs, but this function also handles them correctly.

f=lambda s,n:n*s and s+[x+c for x in f(s,n-1)for c in s]

J, 41 char

   f=.}:@;@({@(,&(<',')@(]#<@[))"1 0>:@i.@])

   'ab' f 3
a,b,aa,ab,ba,bb,aaa,aab,aba,abb,baa,bab,bba,bbb

APL (Dyalog Unicode), 13 bytes^SBCS

⊃,/,¨∘.,\⎕⍴⊂⍞

Try it online!

never miss an opportunity to use a scan :)

prompts for a string of "digits" and then for n

thanks @Adám for telling me how to enable ]box on TIO