The Romanian Football Federation (FRF) confirmed Mutu in the job on Wednesday, after successful talks with president Razvan Burleanu.
It means the 41-year-old former Juventus, Fiorentina and Chelsea forward assumes control of a side who are in the frame to qualify for the Euro 2021 finals.
"I feel honoured, it is a big responsibility for me," said Mutu, quoted on the FRF website.
The Romania Under-21 side were semi-finalists at Euro 2019, where they beat Croatia and England and drew with France before losing to Germany in the semi-finals.
He takes over from Mirel Radoi, who in November was rewarded for his success by being appointed head coach of the senior Romania team.
Mutu said: "I'm coming after Mirel Radoi, who made history with the national Under-21s, and this motivates me even more. This is a talented new generation, this campaign started well. The objective is qualification for the Euros."
Mutu has previously had a short spell as boss of Romanian club side Voluntari and has also coached the Al Wahda reserve team in Abu Dhabi.
The Romania Under-21 side sit second in their Euro 2021 qualifying group, behind leaders Denmark.