No fee was disclosed, but British media reports said the move was worth £43 million ($57 million), with the 21-year-old signing a contract until 2033.
Chelsea finished a disappointing tenth in the Premier League last season but are looking to rebuild under new manager Xabi Alonso.
Reports in Italy suggested Palestra was on the verge of joining Inter Milan before Chelsea made him a better offer.
"A lot of things convinced me to join Chelsea, one of the best clubs in the world," Palestra, named Serie A Defender of the Year for the 2025/26 campaign, told the London side's website.
"I'm very excited to get started. I've felt the energy since the first day Chelsea wanted me. I can't wait to start, see all the fans, my team-mates and the manager."
He added: "We have so many talented players here, a very strong squad and manager in Xabi. He has spoken to me about how he wants us to play, which is exciting, and we can't wait to compete in the Premier League."
Palestra enjoyed an impressive 2025/26 campaign on loan at Cagliari, featuring as a full-back and wing-back.
He made his international debut during Italy's unsuccessful World Cup qualifying play-offs.
Alonso looks as if he will have a much-changed defence to work with following Chelsea's woes at the back last season.
Marc Cucurella has already left for Real Madrid while Chelsea are reported to be considering a bid for Crystal Palace central defender Maxence Lacroix.
