The Portugal U21 striker has signed for the Turks on a two-year loan for a fee of €1 million.
Bebe said: "Sir Alex Ferguson has had a big role in my career. He trusted me and signed me for a lot of money. I tried to show my worth, but I lost confidence.
"When this transfer proposal came to me, I thought 'yes'. I will be joining the best team in Turkey.
"My only thoughts now are to make sure Sir Alex Ferguson has not wasted his trust or confidence."