It is chosen by members of the Academy of Motion Picture Arts and Sciences. You must be invited by the Academy to become a member. Different branches of the Academy (focusing on different aspects of the filmmaking world) have their own standards of eligibility for potential members.
Members of the academy, including actors, producers, directors and a variety of other film craftsmen, choose who will receive the awards that year by casting ballots.
So when a winner thanks the academy, he or she is really thanking all their professional peers who collectively decided to bestow the honor. They're also thanking the organization as a whole, which decided to hand out awards in the first place.