Dembélé signed for Fulham aged sixteen, in August 2012, from Paris Saint-Germain. He became a regular in the Fulham U18 team and won the Premier Academy League in his first season with the club. On 13 September 2015, Dembélé scored his first league goal for Fulham in a 2–1 win against Blackburn Rovers. He scored a brace in a 4–2 win against Reading on 24 October as Fulham overcame a 0–2 deficit to win 4–2. Dembélé scored twice again in the following match a week later as Fulham beat Bristol City 4–1. By the end of the calendar year, he had totalled ten goals for the season.
Dembélé was also part of the France under-19 squad which reached the semi-finals of the 2015 European Championship, scoring in group stage victories over Ukraine and the hosts.
Dembélé joined Celtic in the summer of 2016 as the first signing of the club’s new manager, Brendan Rodgers.