The coalition "agreed to name Giorgi Kvirikashvili's candidacy for the post of prime minister," the leader of the Georgian Dream coalition's parliamentary majority group, lawmaker Zviad Kvachantiradze, said in a televised statement.
Kvirikashvili has also served as foreign minister since September.
President Giorgi Margvelashvili is to formally submit Kvirikashvili's candidacy to the parliament.
The prime minister-designate will then nominate a new cabinet to be confirmed by the legislature.
Garibashvili resigned on Wednesday after just two years on the job without explaining his decision.
Vice premier Kvirikashvili, 48, is a close ally of former prime minister and billionaire tycoon Bidzina Ivanishvili.
He headed Ivanishvili's Cartu bank from 2006 until his appointment as economy minister in 2013.
In line with the Georgian constitution, Garibashvili's resignation led to the dismissal of the entire cabinet which is serving on an interim basis until a new prime minister is appointed.
Georgian Dream - a motley coalition of small parties assembled by Ivanishvili - wrested power from fervently pro-Western Mikheil Saakashvili's United National Movement in the October 2012 parliamentary election.
