Here's why we know this:
* His passion for the job: Harry loves the thrill of the chase and actively sought out dangerous situations throughout his childhood. This aligns well with the Auror role, which involves confronting dark magic and dangerous criminals.
* His skills: Harry is a natural wizard with an incredible talent for Defense Against the Dark Arts and has experience fighting dark wizards like Voldemort. He's also a skilled detective, as seen in his investigations of the Horcruxes.
* The epilogue: The epilogue of Deathly Hallows depicts Harry sending his youngest son Albus to Hogwarts on the same platform he used to go as a child. This implies Harry is working for the Ministry, as only someone with a high position would have such access.
While his job isn't explicitly mentioned, the clues in the books point toward Harry fulfilling his lifelong ambition and becoming a highly respected Auror.