Christian Gourcuff stood down as coach of Algeria on Sunday with more than two years to go before the end of his contract.
The Algerian Football Federation announced his departure on its official website, saying that it had "ended his contract amicably at his request."
According to local reports, the Frenchman had told his bosses of his wish to leave on Thursday, on the plane back from their Africa Cup of Nations match in Ethiopia.
The former France international was appointed in 2014 and speculation surrounding his position had been growing for some time.
The Algerian Football Federation confirmed that Nabil Neghiz - the team's assistant national coach - would take interim charge of the Desert Foxes.
After three wins and a draw, Algeria are top of their qualifying group for the 2017 Africa Cup of Nations.
They need just one win from their remaining games, at Seychelles on 3 June and at home to Lesotho on 2 September, to guarantee qualification.
Algeria are also into the final group stage of 2018 World Cup qualifying.
The draw takes place in Cairo on 24 June 2016, with the final round starting in October.