The arrival of the 39-year-old midfielder was confirmed by the newly appointed Milan coach Massimiliano Allegri earlier this month.
“Very happy to be here to start a new chapter in my career,” said Modric, who will be 40 in an Instagram video in September 40 shared by Milan.
Modric will wear the number 14 shirt, Milan said in a statement.
“It is a huge honor for them to compare myself with (Cruyff) … I was wearing no. 14 at Tottenham in honor of him, and because it was not available to 10,” Modric said after winning the Ballon d'Or prize in 2018.
Modric, considered one of the greatest midfielders of all time, announced in May that he would really leave after Club's World Cup. He made 597 performances for the Spanish club and won 28 trophies, including four LaLiga and six Champions League titles.
He played his last game for Real on Wednesday and came up as a second half replacement during a 4-0 loss for Paris St Germain in the semi-final of the Club World Cup.
“It's a bitter end … he is a legend of world football and from Real Madrid. He will be remembered for many more good things than for the 25 minutes he played today,” said Real Madrid manager Xabi Alonso after the game.
Generally considered the largest player in Croatia of all time, he represented the country 188 times and scored 28 goals. He won the Golden Ball at the 2018 World Cup, where he led Croatia to the final for the first time.
He also won the Ballon d'Or in the same year and became the first player other than Lionel Messi and Cristiano Ronaldo to win the prestigious annual prize since 2007.
The arrival of Modric reinforces a midfield of Milan with also Youssouf Fofana, Yunus Musah and Ruben Loftus-Cheek, with Samual Ricci who came from Torino earlier this month.
Milan, who was not eligible for a European competition after he was eighth last season in the Italian top class of the Top-Flight League, start with their Serie A campaign against newly promoted Cremonese on August 23.