"After a meeting with Jose Nestor Pekerman, the coach has expressed his desire not to continue as the head of the national side," the FCF said in a short statement.
"We at the FCF are proud to have counted on the coach, who qualified us for the World Cups in Brazil in 2014 and Russia in 2018."
Pekerman, who took over in 2012, was not expected to continue after a World Cup campaign that ended with a penalty shootout defeat by England.
He ends his reign with a record of 42 wins, 20 draws and 16 defeats in 78 matches.
"I am very happy and I always want the best for the team in the future," Pekerman told a news conference. "There were no disagreements."
The 69-year old could now be a candidate for the vacant jobs with Mexico or Argentina, the country where he was born and whose Under-20 side he took to the World Cup three times - 1995, 1997 and 2001.
Pekerman also led his homeland at the World Cup in Germany, where the hosts knocked them out in the quarter-finals on penalties.
Interim coach Arturo Reyes will lead Colombia in friendlies against Venezuela in Miami on Sept. 7 and Argentina in New Jersey four days later.
(Reporting by Andrew Downie; Editing by Ken Ferris)
