The Bundesliga side have paid €26.5m for Shick, who cost Roma around €42m in 2017.
Roma will receive 10% of any profit Leverkusen earn from a future sale.
— Bayer 04 Leverkusen (@bayer04fussball) September 8, 2020
24-year-old Schick has signed a five-year contract with Leverkusen and will wear the number 14 shirt.
Schick scored 10 goals in 28 games for Leipzig, compared to eight goals in 58 appearances for Roma.