The Italian international joins Xabi Alonso's Chelsea in a deal worth €60 million including bonuses, with Atalanta having turned down competition from Inter Milan in the final stages of negotiations. The fee represents a significant profit on the player, who spent last season on loan at Cagliari and was named Serie A Defender of the Year.
Palestra becomes Chelsea's first major signing of the Alonso era and arrives having been capped twice for Italy. He is a right-sided wing-back capable of playing in either a back five or a back four, giving Alonso flexibility in his defensive shape.
Inter Milan had been in discussions for several weeks and appeared to be leading the race before Chelsea accelerated their approach and secured agreement with both Atalanta and the player.
Palestra's willingness to choose Stamford Bridge over Serie A was confirmed by former Cagliari sporting director Guido Angelozzi, who signed him on loan and remains one of his advocates: "They followed him closely and saw he is suited to the English game. In his role he is a top-class player."
Palestra came through the Atalanta academy and was regarded as one of the most promising right wing-backs in Italian football. His season at Cagliari gave him 37 senior appearances at the top level and the individual award that confirmed his potential.
Chelsea are paying a premium but acquiring a player at 21 who has already proven himself in Serie A, with years of development ahead of him under one of the most tactically inventive coaches in the game.
Alonso officially takes charge at Chelsea on July 1. Palestra's medical on Friday is a formality, with personal terms long agreed.