There's no definitive answer because no one ever confessed or was arrested for Anastasia's murder. Gambino was the obvious beneficiary. But, the finger points to Genovese. When he returned to the US from Italy after WWII, he thought he should have been Don of the family that Frank Costello headed. But, Costello was protected by solid alliances with stone killers--first Willie Moretti and then Anastasia. So, Genovese thought that, by killing Costello's strongest ally, he could force Uncle Frank to step down.

Some writers claim that Joe Profaci ordered the Anastasia hit, probably because Crazy Joe Gallo, who was in his family at the time, was one of the shooters. But, Profaci had no obvious reason to order the assassination.