The 23-year-old, who joined Kotoko from Berekum Chelsea last season, struggled to impress in his maiden campaign and terminated his contract on Monday by mutual consent despite having two years left.
Ofori expressed his excitement after penning his contract and explained why he opted for Medeama despite the numerous offers on his table.
"I am happy to be here because it's a new challenge and great opportunity to have my career on track," Ofori told Goal.
"Things weren't successful during my one-year stay with Kotoko but everything happens to give us a lesson. I have learnt whatever I needed to know and hope to get my career back to prove a point that I'm still a top player. There were numerous offers but Medeama were serious with theirs and their terms were favourable too.
Ofori has become the third player from Kotoko after goalkeeper Eric Ofori Antwi and Theophilus Nyame to join the Yellow and Mauve in the transfer window. He will also team up with former mate at Chelsea Latif Salifu, who signed a three-year contract with the club last month.
The league will kick off on February 11 and he is likely to make his debut against Wafa at home.