Financial details of the deal were not disclosed, but British media reported that Chelsea had paid Rennes about €27.5 million ($30.15 million) for the 19-year-old.
Ugochukwu, a France under-19 international, was a regular at Rennes last season, helping the club finish fourth in the French top flight and make 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 co-sporting directors Laurence Stewart and Paul Winstanley told the club website.
"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.