Financial details of the deal were not disclosed, but it has been reported that Chelsea had paid Rennes about £23.5 million for the player.
Ugochukwu, a France U19 international, was a regular at Rennes last season, helping the club finish fourth in the French top flight and making the Europa League knockout stage.
"We're delighted Lesley is joining Chelsea. He is an impressive young player who has already made his mark in Ligue 1," Chelsea's co-sporting directors Laurence Stewart and Paul Winstanley said.
"He has a huge amount of potential and we know he is going to continue to develop and improve. We are pleased that he has joined us (on tour) in the U.S. and that he will be able to integrate with the squad quickly."
Ugochukwu joined the Rennes youth system aged eight and made his senior debut just after his 17th birthday, becoming the club's fourth-youngest debutant at the time.
