From the top answer on this question: What are Harry, Ginny, Ron and Hermione's professions?
Harry became an Auror under the new Minister of magic Kingsley Shacklebolt and Ginny became a professional Quidditch player for the Holyhead Harpies.
Harry Potter, who always voiced a desire to become an Auror, or someone who fights dark wizards, was named head of the Auror Department under the new wizarding government headed by his friend and ally, Kingsley Shacklebolt.
JKR has also stated that Ron and Harry never went back and graduated:
SU: Oh, speaking of Ron/Hermione—
JKR: Yeah, did they graduate from Hogwarts?
SU: Yes, did they?
JKR: Harry and Ron didn't go back, Hermione did. Did you bet right? You must've, I mean, come on. No one's gonna think Hermione wouldn't go back.
However, McGonagall in OtP states the requirements for becoming an Auror:
You'd need top grades for that,... They ask for a minimum of five N.E.W.T.s, and nothing under 'Exceeds Expectations' grade, I see. Then you would be required to undergo a stringent series of character and aptitude tests at the Auror office. It's a difficult career path,... they only take the best
Now I will admit, destroying the Horcruxes and then Voldy is probably enough resume anyone needs, but is there a canon reason stating how Harry and Ron became Aurors without graduating and taking/passing N.E.W.T. exams?