Sitting beside Gurgenidze, Saakashvili said: "When Lado was appointed a year ago he told me he would be able to do this just for one year.
"Now we face new challenges. New power and new energy are needed to address these challenges.
"Our economy is under twin assault, from the global financial crisis and the Russian aggression."
Gurgenidze said it was "a joint, consensual decision".
"I have no doubt about the continuity of liberal economic policies in Georgia, which have driven Georgia's success over recent years," he said.
Officials said the prime minister-designate would reveal his cabinet before a parliamentary debate. The date of the debate is yet to be announced.
Saakashvili said there would be no radical changes to the cabinet.
Gurgenidze, a 37-year-old technocrat and former banker, became prime minister in November 2007, with the task of attracting foreign investment and maintaining economic growth.
But the August war has hit investor confidence and reined in otherwise healthy growth forecasts.
Georgia's pro-Western president, who came to power in the 2003 "Rose Revolution", is facing growing criticism from opponents who accuse him of walking into a war Georgia could not win.
Some opposition factions have announced a protest for November 7, the first anniversary of a police crackdown against opposition demonstrators that shocked Georgia's Western backers.
Critics of Saakashvili say he has fallen short on promises to open up Georgia's democracy and increase media freedom.
Nino Burjanadze, a co-author of the Rose Revolution who split with Saakashvili this year, said she would form her own party to challenge the government.
Speaking to a news conference, she said: "We have an authoritarian regime in Georgia rather than a democratic state."