The head of Georgia's Supreme Court, Kote Kemularia, becomes justice minister and vice-premier.
Parliament, where Saakashvili's supporters have a majority, approved the government line-up by 175 votes to 24.
Nogaideli, 40, served as finance minister under Shevardnadze for 18 months until late 2001. He returned to the job under Saakashvili. He was close to Zhvania and has been credited for dramatically boosting revenues and reforming the tax system.
Chechelashvili, 43, has also served as Georgia's ambassador to Ukraine and Moldova.
Zhvania, 41, was the most able political operator in Saakashvili's team and analysts have expressed concern the promising start made in reforming Georgia, an impoverished ex-Soviet state, could be derailed by his death. He, Saakashvili and parliamentary speaker Nino Burjanadze were the trio of Western-oriented reformers who led the November 2003 mass protests that overthrew Shevardnadze's administration.