The teenage forward was a free agent following the expiry of his contract and has penned a four-year deal with his new club.
Dembele featured twice last season under Ange Postecoglou, taking his tally to ten appearances for Celtic. However, his campaign was hampered by an ankle injury.
The 19-year-old hit the headlines at 15-years-old when he trained with the first-team under Brendan Rodgers and made his debut at 16.
He was at the centre of much attention at international level, playing for both Scotland and England coming up the youth ranks.
Dembele will now continue his career in France with the side who finished 11th in last season’s Ligue 1.
Brest referred to the forward as a “precocious player” who arrives “with the desire to impose himself in a new team and a new championship.”
Dembele was attracted to the club following discussions with the club's sporting director.
“I come to Brest because I saw that the project presented by [sporting director] Greg Lorenzi was good,” he said. "It's something that suits me and I think I can have some playing time here.
"It was a great opportunity that presented itself to me and it interested me”.
He added: “I'm very explosive, I like to have fun and give it to the fans and of course I like to score and win”.
Meanwhile, Celtic are continuing to look to strengthen the squad ahead of a return to league action at the end of the month and the Champions League group stages in September.
They play their first pre-season friendly on Wednesday.