The 22-year-old Italy international, who has struggled with injuries since his emergence in the Milan first team, arrives at the Stade Louis II on a season-long loan, with the principality club holding an option to buy.
The striker made over 100 appearances for the Rossoneri in all competitions since joining from Genoa in 2011 but spoke of his delight at his new challenge
"It's a great feeling to sign here in the principality," he told the club's official website as the news was made official. "I'm very happy. I would like to thank the president of AS Monaco for this chance.
"I hope to have a great season with Monaco and to give pleasure to the fans."
Monaco's vice president Vadim Vasilyev believes the club have made a statement with the lucrative signing.
"We're very proud to welcome Stephan El Shaarawy, whose arrival marks a high point in our recruitment strategy," he said.
"He has several seasons experience at a high level but at the same time represents the future. His talent permitted him to explode into the eyes of the footballing world some time ago and we're convinced that Monaco will allow him to reach his full potential."
El Shaarawy made 14 Serie A starts for Milan last season, scoring three goals and setting up a further three.