The 19-year will join David Unsworth's U23 squad.
Mathis, who is a product of Lyon's academy, hopes to one day to play for the first team.
"My dream is to play for the first team here," Mathis told the club's official website.
"I want to play in the Premier League for Everton.
"It is a great club and I have always liked English football and the Premier League. Ronald Koeman is a huge figure, not only as a coach now but his reputation as a player speaks for itself as well."
| Young French striker Boris Mathis has joined on a two-year contract & will link up with #EFCU23 for pre-season. https://t.co/oz90fXjrSRpic.twitter.com/lHSVJroTuI
— Everton (@Everton) July 5, 2017