The 24-year-old has joined the Rossoneri for a contract worth about 20 million euros ($22.00 million) plus eight million euros in add-ons, according to Italian media.
Chukwueze made his Villarreal debut in 2018 and scored 37 goals with 31 assists in 207 appearances in all competitions. He won the Europa League with the Spanish outfit in 2021.
He has been capped 28 times and has scored four goals for his country, having made his debut in 2018.
Chukwueze will wear the number 21 shirt at Milan.