Several hundred City fans were at the stadium on Saturday evening to welcome Adebayor.
"It made me feel really welcome and special and I can't wait to play for City's fans and show them what I can do," said Adebayor, who, as at Arsenal, will wear the number 25 shirt.
"I was born to play football and that is what I want to do. I have come here to make history for this club and those supporters.
"It is what the chairman and the manager told me that they want too and I can't wait to get started."
City boss Mark Hughes was delighted with his capture.
"Emmanuel has been one of the top forwards in the Premier League since he arrived from France and we are delighted he has agreed to come and join us," the Welshman told the club's official website.
"Along with the other signings we have made in the last two windows he will greatly enhance our ability to compete with the top sides.
"His arrival is another clear indication that we are determined to augment the players we have here with the best of international talent.
"He adds vital balance and power to our attack. He has everything a top forward needs. He is versatile, powerful, quick and agile on the ball.
"I am looking forward to working with him as are the rest of the staff. He will definitely add a new dimension to our play. I have been a great admirer for a long time."