Andre Silva, Hakan Calhanoglu, Mateo Musacchio, Ricardo Rodriguez, Franck Kessie and Fabio Borini have all switched to the San Siro, while coach Vincenzo Montella has agreed a new contract.
Conti, who has has penned a five-year deal at San Siro, won his first full Italy cap in May's friendly thrashing of San Marino.
The Rossoneri have reportedly paid €24 million to secure his services, taking their summer spending past €150m.
The right-back started 31 Serie A games last season as Atalanta finished fourth in the table, two places above Milan, qualifying for the Europa League as a result.
Andrea Conti is at Milanello, ready for his physical tests— AC Milan (@acmilan) July 6, 2017
Andrea Conti è a Milanello, pronto per i suoi test atletici pic.twitter.com/VhTWY9yMTt
Moving the other way from Milan to Atalanta is Matteo Pessina, a 20-year-old left-sided midfielder who featured for Italy at the Under-20 World Cup, the Azzurri reaching the semi-finals before losing to England.
Conti will be reunited with Kessie after the midfielder also left Atalanta for Milan.