The 22-year-old, who can play as a striker and out wide, joins from King’s Lynn Town, who were relegated from the National League last season, for an undisclosed fee.
Talks have been ongoing for a number of weeks but the deal is now complete.
Gyasi said: “I’m excited to get going. It took a while to get done but I’m happy to be here. I want to get my goal tally up as much as possible, come here and enjoy myself.
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“When I scored here [last season] the fans were booing me – the atmosphere was crazy. Hopefully I can get a few more goals.
“I’m quick, good in one-versus-one situations and I score goals. I just want to get going, get as many games as I can and get some goals.”
Gyasi also had interest from National League side Halifax, Scottish Championship club Ayr United and German outfit FC Phonix lübeck, who he has played for before.
Gyasi was loaned out to Dover Athletic in January, bagging five goals in 19 appearances.
He scored against Chesterfield at the Technique Stadium for the Whites. He also notched a hat-trick against Wrexham.
Gyasi, who signed for Chelsea when he was 11, will bring some much-needed pace to the ranks.
He becomes Town’s sixth summer signing after the arrivals of Branden Horton, Bailey Clements, Ryheem Sheckleford, Joe Cook and Darren Oldaker.