The 28-year-old has a year left on his contract at Juventus and was on the verge of signing a four-year deal with the Cimbom during the summer transfer window but negotiations broke down in the eleventh hour.
He has struggled for game time in Massimiliano Allegri's setup, playing only five league matches so far this term.
“We agreed on everything over the summer,” Asamoah was quoted as saying by TuttoJuve.
“After drawn-out negotiations, I made the best decision for myself. I gave my word to Galatasaray [that I'll join them from here] and I won’t go back on it.
“I picked them for the role they gave me in their team and what they offered me.
“Now I’m thinking about Juve, but Galatasaray are important to me and I’m following all their games with great interest.
“Their football is promising and I look forward to becoming a part of this team,” he added.
Asamoah joined Juventus from Udinese in 2012 and has gone on to win five Serie A titles and three Coppa Italia trophies.
However, according to CalcioCarmeto, the Old Lady have denied the existence of any request for departure from the Ghana international.