The decision comes after Galatasaray's chairman Unal Aysal gave his consent for Terim, one of the most successful coaches in Turkish history, to take charge of the national team for their remaining four FIFA World Cup™ qualifiers.
Terim, who is in his third spell with Galatasaray, will not quit his club responsibilities.
The TFF had approached Terim after announcing Wednesday that previous coach Abdullah Avci had left his job "by mutual agreement".
Avci took over the role in November 2011 but has paid for a poor FIFA World Cup qualification campaign that has left the team fourth in Group D.
Turkey have seven points after six games, a long way behind runaway leaders the Netherlands, on a maximum 18 points, and four points behind second placed Hungary, who are currently in the play-off spot.
With four games left they will have a hard job overhauling both Hungary and Romania, who are three points ahead.
"After the results we got, we parted our ways with Avci," TFF President Yildirim Demiroren said at the signing ceremony. "Problems are abound in Turkish football. We thought about an experienced, success-hungry coach who will solve the problems and negotiated with Terim."
He also thanked Galatasaray for allowing Terim to take up his dual coaching responsibilities.
Known as the "Emperor" in his homeland, Terim previously coached Turkey from 1993 to 1996 and then again from 2005 to 2009.
He has won six Turkish league titles with Galatasaray and led them to the UEFA Cup crown in 2000, beating Arsenal on penalties in the final.