The 19-year-old will either join Mauricio Pochettino’s first-team roster or be loaned away, the Blues have not yet decided.
A short-term transfer to Strasbourg, a Ligue 1 team in which Chelsea has the majority of the shares, has been suggested.
Ugochukwu graduated from Rennes’ academy and has since made 60 appearances for the team, including 35 last season across all competitions.
The 19-year-old has six caps for France’s U19 team and primarily operates as a holding midfielder.
With the departures of Mason Mount, Mateo Kovacic, Ruben Loftus-Cheek, and N’Golo Kante this summer, Ugochukwu’s addition would complete the revamp of Chelsea’s midfield.