The financial details were not disclosed but Italian media said the transfer fee was 18 million euros.
"Everyone wanted him. He wanted ONLY us. #BrozovićIsYellow," Al-Nassr wrote on Twitter.
"Don't worry I'm here. I choose AL-Nassr," the Croatia international said.
Brozovic joined Inter in 2015 and helped them win Serie A in the 2020-21 season followed by two Italian Cup trophies.
He was also in the Inter team that lost the Champions League final to Manchester City last season.
The Saudi Pro League has become an attractive destination for Europe-based players since Cristiano Ronaldo moved to Al-Nassr last January.
League Champions Al-Ittihad signed Ballon d'Or winner Karim Benzema last month along with former Chelsea midfielder N'Golo Kante.
Last month, the Saudi Public Investment Fund (PIF) announced a Sports Clubs Investment and Privatization Project involving the league champions Al-Ittihad, Al-Ahli, Al-Nassr and Al-Hilal.
PIF own 75% of each of the four clubs, while their respective non-profit foundations own 25% of each.
