Sunderland signed the 24-year-old in a club record move in excess of £13million.
Gyan has signed a four-year contract with the Black Cats.
“It’s been a long day, but finally I’m happy to be here and my family and friends are also happy for me,” Gyan told the club’s official website.
“My family is in England already and I am happy this is the right place for me.
“The Sunderland coach has faith in me because he has been following me for two years now.
“I am pleased I have the opportunity to come to England.”
He added: “I follow English football and I know Sunderland have incredible fans.
“I especially know about the derby when they play against Newcastle. That is something incredible. I have witnessed that myself.
“The Sunderland fans never say die. They keep cheering their team on for 90 minutes. That gives me confidence to play maximum football.
“I am here to do my best and show what I can do. I have watched Sunderland play before – I think it will be good.”
