"Coming from Italy's eagles. Savic represents Asia's Leader," Al-Hilal said on their Twitter account.
Italian media reported that Al-Hilal would pay around 40 million euros ($44.51 million) for the player.
Milinkovic-Savic has signed a three-year contract with an option for a fourth and will be teammates with Senegal defender Kalidou Koulibaly and Portugal midfielder Ruben Neves, both of whom joined the club in June.
Al-Hilal posted a video of Milinkovic-Savic's father looking at photos of his son who is then pictured in his new team's jersey.
"I'm Hilal" the Serbian player said.
Earlier this month, Al-Hilal reappointed Portuguese coach Jorge Jesus on a one-year deal.
Milinkovic-Savic joined Lazio in 2015 and helped them win the Italian Cup in the 2018-19 season and two Italian Super Cups.
Al-Hilal are the most decorated club in Saudi Arabia and Asia, and hold the record for the most Saudi League and Asian Champions titles with 18 and four, respectively.
The Riyadh-based club lost their league and Champions League crowns and ended up third in last season's Saudi Pro League.
