The 31-year-old has signed a four-year deal with Milan who brought him in to replace departed Olivier Giroud following the former France international's transfer to Los Angeles FC.
"Morata has signed with the Rossoneri until 30 June 2028, with an option to extend for an additional year," said Milan in a statement.
Italian media report that Milan paid Morata's 13-million euro ($14.2 million) release clause and that the player will earn around 4.5 million euros per season.
Morata played in every match in Spain's triumph at the Euros, netting his only goal of the tournament in La Roja's 3-0 thumping of Croatia which kicked off their campaign in Germany.
He has scored 36 goals in 80 international appearances for his country.
Morata returns to Italy after two spells with Milan's rivals Juventus, where he won two league titles and three Italian Cups.
Morata has also won the FA Cup with Chelsea and featured in two triumphant Champions League campaigns with Real Madrid, in 2014 annd 2017.
Milan, who finished second in Serie A last season but 19 points behind champions Inter Milan, begin the league season under new coach Paulo Fonseca with the visit of Torino on August 17.
