"It's a fantastic signing for us," he said. "It's a hell of a lot of money in today's climate but the owner understood the necessity and we've managed to bring in another top class striker. We're making huge strides.
"I tried to sign him last summer but it wasn't possible."
Gyan said he was pleased to have joined the Black Cats and praised the fans for their "never say die" attitude.
Gyan blasts penalty against bar
"I follow English football and I know Sunderland have incredible fans," added the forward, who has scored 22 goals in 44 games for Ghana.
"I know about the derby against Newcastle. That is something incredible. I have witnessed that myself.
"The Sunderland fans never say die. They keep cheering on for 90 minutes. That gives me confidence to play maximum football."
Gyan began his career with Liberty Professionals in Ghana before moving to Italian side Udinese in 2003.
In 2008, French outfit Rennes paid Udinese 8m euros (about £6.6m) for the striker who went on to score 14 goals in 47 appearances.
Sunderland also confirmed that midfielder Teemu Tainio has left the club.
The Finland international's contract has been terminated by mutual consent.
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