President Mikheil Saakashvili proposed to parliament Lado Gurgenidze, chairman of the Bank of Georgia, as Nogaideli's replacement.
Nogaideli, who became premier in February 2005, had cited health reasons for his resignation earlier on Friday.
Georgia was rocked with opposition riots for six days earlier this month as protestors occupied central Tbilisi demanding the resignation of President Mikheil Saakashvili. The Georgian leader responded by sending in police to crack down on protesters on November 7, later declaring a state of emergency, which was lifted on Friday evening.
On November 8, Saakashvili announced early presidential elections for January 5, 2008.
Commenting on his possible appointment as prime minister, Gurgenidze said he would focus on social projects and employment.
"I see my main task, if I am appointed, as to establish a dialogue and secure a consensus between socially vulnerable segments of the population and three main groups of people," Gurgenidze said, adding that these groups were Georgian businessmen, investors and Georgians abroad.
Under the Georgian Constitution, the prime minister's resignation automatically means the resignation of all cabinet ministers. The outgoing government in Georgia includes 13 ministers and four state ministers.