"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 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.
Interim coach Arturo Reyes will lead Colombia in friendlies against Venezuela in Miami on September 8 and Argentina in New Jersey four days later.
