The 19-year-old will finish the season on loan at the Ligue 1 club where he has established himself as an attacking full-back since coming through the youth ranks.
Gusto has made 54 appearances for his hometown club and Chelsea view him as long-term competition for Reece James.
Gusto described himself as a "box-to-box" player in a short video on Chelsea's website.
"I choose Chelsea because it's a big club and I like the project," he said. "I'm very happy to be here."
The reported £26.3million fee Chelsea will pay for Gusto adds to an already expensive January at Stamford Bridge.
With Graham Potter's side still struggling with an extensive injury list, Chelsea have already signed Mykhaylo Mudryk, David Datro Fofana, Benoit Badiashile, Noni Madueke and Andrey Santos on permanent deals and brought in Joao Felix on loan from Atletico Madrid this month.
They are also expected to announce a deal for RB Leipzig forward Christopher Nkunku to join in a £50million plus move in the summer.
In line with the recent pattern at Chelsea, Gusto has agreed a long-term contract which runs until the summer of 2030.
After Mudryk signed an eight-and-a-half year deal, questions have been raised about Chelsea's use of long-term contracts to spread the cost of their extensive rebuild.
Gusto is the 16th first-team signing since Todd Boehly bought the club last year, with spending now over the £400million mark.