Answer: He remains on Pandora, and his consciousness is transferred to his avatar.
Jake decides to remain on Pandora with Neytiri as part of the Omaticaya clan. Among those humans who are also allowed to stay are Norm Spellman and Max Patel, the scientists from the Avatar Program who previously allied themselves with Jake. In his final video log that he records at the now-abandoned RDA base, Jake explains that no matter what happens, he does not intend to return to "this place". His last words before signing off provide a hint to his destiny: "I guess I better go. I don't want to be late for my own party. It's my birthday, after all." The scene then shifts to the Tree of Souls, where Mo'at is leading the Omaticaya in a ceremony not unlike the one performed during the failed attempt at saving Grace's life. Thankfully, the outcome of the ceremony is different this time, and Jake's consciousness is successfully transferred from his human body to his avatar body. The movie ends on a close-up of Jake's avatar as he opens his eyes.