The Brazilian has been at Shakhtar for eight years, winning the Europa League, six Ukrainian championships and four cup titles and scoring 129 goals in all competitions.
Last season, he netted nine times, including hat-tricks in successive games in the Champions League to finish one behind joint top scorers Neymar, Lionel Messi and Cristiano Ronaldo.
Previously, he was at Porto Alegre side Internacional where he won a Club World Cup medal in 2006.
The 28-year-old has played four matches for Brazil, having made his debut in last year's 4-0 friendly win over Turkey.
"FC Shakhtar thanks Luiz Adriano for the years he has spent in the team, for the goals scored and records set," said the club in a statement. "We wish Luiz Adriano good luck in his new club and beautiful victories."
Milan confirmed they had signed him on a four-year contract.
(Writing by Brian Homewood in Berne; Editing by Ken Ferris)
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