Kamara, 22, scored 11 goals in 29 games last season to help the French side win promotion from Ligue 2.
The Championship club have an option to extend the former Monaco trainee's contract by a further 12 months at the end of his deal.
"Aboubakar brings exceptional speed and finishing ability up top," said Fulham vice chairman Tony Khan.
"It's no secret that we've had interest in Aboubakar for some time, and I'm confident that it won't take long for our supporters to see why."
Fulham start the new Championship season at home to Norwich City on Saturday.
Find all the latest football transfers on our dedicated page.
Fulham have signed SC Amiens striker Aboubakar Kamara on a four-year deal for an undisclosed fee.