Cornet joins the Premier League side after a successful seven-year stint with Lyon, in which he scored 51 goals.
According to reports, his deal is said to be around the range of £15m.
During his time at Lyon, Cornet also helped the club secure top-four finishes and regular entry into the UEFA Champions League.
In August last year, Cornet also scored the opening goal in a 3-1 victory that knocked Manchester City out of the quarter-finals in the 2019/20 UEFA Champions League.
Commenting on the agreement, Maxwell Cornet said, “I am excited to be joining Burnley in the Premier League and to play with and against many of the greatest players in the world.
“I have developed the greatest respect for Burnley and what the club has done. I welcome the challenge of hard work and am fully committed to doing what I can to contribute. I look forward to what we can achieve.”
Alan Pace, Chairman of Burnley FC, said: “On behalf of everyone at Burnley Football Club, I’d like to wish Maxwel a warm welcome to the Clarets’ family.”
He further added, “We’re delighted to have secured such a talented player with Champions League pedigree and we look forward to him joining up with Sean and the team.
“The wide position was identified as in need of strengthening and we saw Maxwell as the ideal player to fulfill this with talent, versatility, and pace.”
The five-year deal is considered to be one the largest transfer deals in Burnley’s history and will see the 24-year-old play in several attacking and defensive roles on either flank and will be seen linking up with Sean Dyche’s squad following the international break.
The signing of Cornet follows the arrival of the 20-year-old centre-back Nathan Collins from Stoke.