The 19-year-old has signed a contract at Stamford Bridge to the summer of 2030 but will finish the current season back in Ligue 1 with Lyon on loan.
Chelsea will pay a reported £26.3 million ($32.6 million) for Gusto, who came through the ranks at Lyon and made his senior debut in January 2021.
Gusto is the seventh signing of a busy January window for Chelsea, who have already brought in Mykhaylo Mudryk, David Datro Fofana, Benoit Badiashile, Noni Madueke and Andrey Santos on permanent deals and signed Joao Felix on loan from Atletico Madrid.
He fully established himself in the first team last season with 30 Ligue 1 appearances while also helping his side to the quarter-finals of the Champions League.
Gusto has made a total of 54 appearances for Lyon over three years, and Chelsea see him as long-term competition for Reece James at right-back.
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