18-year-old Alajbegovic, who spent last season at RB Salzburg and scored 13 goals in 44 appearances across all competitions, has signed a five-year contract with Juve.
He scored in Bosnia's penalty shootout wins over Wales and Italy in the World Cup playoffs and netted the opening goal in the 3-1 victory over Qatar that sent them through to the knockout stages for the first time, where they lost 2-0 to co-hosts the United States.
Alajbegovic, born in Germany, joined Salzburg from Leverkusen, where he had been with the youth academy since 2021, before the German club re-signed him on a five-year contract.