The 26-year-old’s deal was confirmed in a statement by his Italian club on Tuesday.
“After more than seven seasons together, everyone at Udinese Calcio wished Emmanuel all the best,” it read.
With English Championship side Birmingham City lurking, Bursaspor refocused negotiations to a loan option and had their bid accepted.
Ghana international Badu is joining the green crocodiles until June 2018, as he is under contract with Udinese until June 2020.
Agyemang-Badu has been with the Friuli-based side since January 2010.
He adds to the growing list of Ghanaian players in Turkey. It is understood that Bursaspor are turning their attention to another Black Stars player, David Accam after failing to land Asamoah Gyan who opted to join rivals Kayserispor recently.
From Sammy Heywood Okine