The announcement came during the annual meeting of the International Council of the World Evangelical Alliance in New York.
Dr Tunnicliffe has had one of the longest tenures in the history of the WEA, ending his second five-year term this year on December 31.
"It has been a great privilege for me to serve as Secretary General of the WEA for the past ten years as part of a great team of both the International Council and staff," said Dr Tunnicliffe.
"I believe the future of the WEA has never been brighter as we experience unprecedented opportunities for global Kingdom impact."
The WEA said in a media update that Dr Tunnicliffe's contribution to the global organisation had been "outstanding" and left it "immeasurably stronger" than when he took up the role in 2005.
The Reverend Ndaba Mazabane, Chairman of the International Council, said: "Geoff is leaving the WEA in great shape. His contribution to the work has been outstanding.
"God led Geoff to us in His providence and has now led him to leave the position to younger leadership to take on the role as the WEA moves on to make a renewed contribution to a changing worldwide Church."
The WEA said conversations have started in the International Council about the selection of a new Secretary General.