The 21-year-old has signed a contract through to 2033 and will join his new team-mates for pre-season under manager Xabi Alonso.
Palestra is the first signing of the Xabi Alonso era at Stamford Bridge, and the defender explained why the new Blues boss played such an important part in his decision to move to west London.
"It was very important," Palestra said. "I feel a lot of energy from him. Also, he is one of the best managers in the world [as you can see when] he won at Bayer Leverkusen.
"I have had two conversations with him and I'm very happy because he told me what he wanted from me."
Palestra, who was named Serie A Defender of the Year last season, also spoke of his enthusiasm at joining the club.
"A lot of things convinced me to join Chelsea, one of the best clubs in the world," he said. "I'm very excited to get started. I've felt the energy since the first day Chelsea wanted me.
"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, and we can't wait to compete in the Premier League."
Palestra arrives at Stamford Bridge on the back of an impressive 2025-26 loan campaign at Cagliari, featuring in 37 league games for the Sardinian club.
His performances as a full-back and wing-back on both flanks stood out in the Italian top flight, and he earned his senior Italy debut earlier this year, a first cap quickly followed by a second appearance for the Azzurri.
The defender spent his entire career to date at Atalanta before completing his move to England, and paid tribute to the Bergamo club on social media before the transfer was confirmed.
"I arrived in Bergamo as a boy," he wrote. "Atalanta has been much more than a club: it is the place where I grew as a footballer and as a person."
Palestra thanked the Percassi family, Atalanta's staff, his team-mates and supporters for what he described as an extraordinary path that began 11 years ago.
The 21-year-old made 41 appearances and scored three goals for Atalanta's Under-23 side and 16 appearances for the first team. He has also represented Italy at Under-21, Under-20, Under-19 and Under-18 level, and won the Europa League during his time at the club.