"Our team unanimously supported Irakli Garibashvili's candidacy," Ivanishvili told reporters in the capital Tbilisi.
"Georgia will have a very worthy prime minister."
The 31-year-old will take over on November 24 after being confirmed by parliament, where Ivanishvili's Georgian Dream coalition holds a majority, following the inauguration of a new president.
"I want to thank Bidzina Ivanishvili for the trust he has shown in me. I promise that I will continue his path," Garibashvili said, standing on a podium next to his mentor.
Last week another Ivanishvili ally -- political novice Giorgi Margvelashvili -- won a crushing victory at a presidential election to succeed US ally Mikheil Saakashvili.
Ivanishvili -- who says he has achieved everything he wanted to since defeating arch-foe Sakaashvili's party in parliamentary elections last year -- has long pledged to quit.
He has said he intends to move into civil society after leaving office and denies claims that he will continue to call the shots.
The graduate in international relations from the Sorbonne University in Paris has headed Ivanishvili's charitable foundation and worked at his bank and his rap star son's record label.
