The fight is Joshua’s first since reclaiming his belts from Andy Ruiz in December 2019 in Saudi Arabia.
Both boxers were cautious in the first two rounds with Joshua using more of his jabs.
Pulev has been unbeaten in his last eight fights since losing via knockout to Wladimir Klitschko in 2014. The 39-year-old won 28 of his previous 29 with 14 by way of knockout.
South African referee Deon Dwarte stopped the fight after the ninth round knock down.
Joshua’s victory sets up a potential all-British heavyweight unification bout against Tyson Fury in 2021.