On 3 July 2019, Pukki signed a new three-year contract with the Premier League newcomers. On 9 August, he scored his first Premier League goal in a 4–1 away loss to Liverpool on the opening day of the new season. Eight days later, he scored a hat-trick against Newcastle United in a 3–1 victory, Norwich's first hat-trick in the Premier League since Efan Ekoku against Everton in September 1993. For the month of August he was named the Premier League Player of the Month, and the PFA Premier League Player of the Month. Pukki scored eleven Premier League goals in total for Norwich but was unable to prevent the Canaries from being relegated to the Championship.