The 34-year-old Hrgović weathered Itauma's early dominance and a second-round knockdown before turning the fight around and forcing the Briton's corner to throw in the towel after a barrage of punches in the ninth.
The title had been vacated by Ukrainian Oleksandr Usyk. Hrgović improved his professional record to 21 wins and one loss, while the 21-year-old Itauma suffered his first defeat after 14 wins.
Hrgović, who won Olympic bronze in Rio in 2016 and European gold in 2015 as an amateur, has now added a world heavyweight title to his achievements.