Former Celtic striker Sutton believes that the 19-year-old forward would prove to be a good signing for the Bhoys.
The Englishman has also claimed that that the youngster would not have joined the Hoops had Ronny Deila been in charge of the first team.
Deila left Celtic at the end of the 2015-16 season after two years in charge of the Scottish Premiership champions.
Former Liverpool boss Brendan Rodgers was subsequently appointed the Celtic manager.
“Moussa Dembele arriving at Parkhead is a massive move forward for Celtic,” Sutton wrote in The Daily Record about Dembele.
“I stated in this column a week ago that the club were going to have to start making proper signings to back the Brendan Rodgers feelgood factor – and this is an impressive start.”
“It’s a great signing which, I have to admit, would not have happened without Rodgers,” added Sutton. "Can you tell me that Dembele would have picked Celtic had Ronny Deila still been the manager? No, I doubt it as well. That might sound harsh on Ronny, but it’s a fact.”
Dembele is hugely talented and very promising, and he should prove to be a great signing for Celtic.
The France Under-20 international forward scored 14 goals and created 42 chances in 42 Championship appearances for Fulham last season.
During the 2014-15 campaign, the teenager created three chances in 11 matches for the Cottagers.
Rodgers has a good track record of working with talented young players, and Dembele should be relishing the chance to play under him.