The Atalanta wing-back has joined The Blues in a £43 million deal with an option to extend for a further year to 2033, as per transfer expert Fabrizio Romano.
The deal comes after Palestra flew into London on Thursday to undergo his medical with the Premier League club.
The 21-year-old spent last season on loan at Cagliari from Atalanta, making 37 appearances in Serie A.
Palestra scored once and provided four assists for the Rossoblu during the 2025/26 campaign.
It becomes the fifth summer signing under new boss Xabi Alonso, having already brought in Emmanuel Emegha, Dastan Satpaev, Denner and Geovany Quenda.
The Italy U21 international has been brought to suit Alonso’s 3-5-2 system perfectly, which utilises wing-backs who will play high up the pitch to stretch defences.
While other top clubs across Europe had been circling for Palestra’s signature, including long-time admirers Inter and Manchester City, the wing-back will be playing his football at Stamford Bridge next season at Chelsea.