Atletico says that the 30-year-old centre-back will play for the Nerazzurri after the two clubs reached a deal.
Miranda spent four seasons at Atletico, helping them win the Spanish league, Europa League and Copa del Rey.
The player had been tipped with a move to England with Chelsea and Manchester United understood to be interested in him, but Miranda has opted for a move to Italy instead.
Atletico said on their official website that Miranda “will always be remembered by Atletico’s fans for his goal that gave us the 2013 Copa del Rey” in the final against fierce rival Real Madrid.
Atletico has already sold striker Mario Mandzukic to Italian champion Juventus, replacing him with Jackson Martinez from FC Porto.