It depends on the context. Here are some examples from my experience:
Congratulations for/on + (-ing)
e.g. "Congratulations for/on finishing your degree"
Congratulations to + (person)
e.g. "Congratulations to you for finishing your degree"
Congratulations on + (noun)
e.g. "Congratulations on your degree"
Hope that helps!
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Congratulations on the birth of your baby/ graduating with honors.
Congratulations for being selected for the program.
Please convey my congratulations to your dad for completing the marathon.