The former Under-17 boss' first task is to guide his country's senior team throughout the qualifying campaign for World Cup 2014
The 48-year-old will take over from Guus Hiddink, whose contract was terminated on Tuesday after failing to guide Turkey to the Euro 2012 finals following a 3-0 aggregate loss to Croatia in the play-offs.
Avci, who has been in charge of Istanbul B.B. since 2006, will return to international management after leading Turkey's Under-17 squad to glory at the European Championship in 2005.
"I am very happy with this opportunity," Avci said during his presentation. "We will make important moves for Turkish football."
Turkey have been drawn with the Netherlands, Hungary, Romania, Estonia and Andorra in the qualifiers for World Cup 2014.