The 50-year-old had been in charge of the national side since November 2011 but had struggled to meet the growing expectations of the federation and Turkey supporters.
Turkey sit in fourth place in Group D of their World Cup qualifying group with just two wins from their opening six matches, leaving them four points behind second-placed Hungary and 11 points behind leaders Netherlands.
With their chances of reaching Brazil in 2014 all but over, both parties have now agreed that Avci will step down, with a statement on the Turkish Footall Federation's website confirming the news.
"Abdullah Avci is leaving the national team after reciprocal talks and an agreement was reached. We thank Mr Avci for his services," read the statement.
The coach himself added that the decision was in the best interests of everyone concerned.
"Just like winning and losing, parting ways is also a part of football," he told the Hurriyet Daily News. "I consider that quitting my post is the right decision."
Galatasaray boss Fatih Terim is rumoured to have been approached by the Turkish FA to succeed Avci at the helm of the national team.
Turkey face Andorra in their next World Cup qualifier on September 6, before a trip to Romania four days later.