[4] Meslier began playing football with his local club Merlevenez at the age of 6, and after a successful match against FC Lorient joined their academy.

With his form helping Lorient finish in 6th in 2018–19 Ligue 2 but narrowly missing out on the playoffs due to goal difference compared with RC Lens.

[17] With Meslier putting in an impressive performance against the Premier League side in a 1–0 defeat on his debut, he was praised for his distribution and his saves during the match.

[21][22] On 23 July 2020, Meslier joined Leeds permanently following their promotion to the English Premier League, for a reported £5m transfer fee,[23] signing a three-year contract.

[24] Meslier made his 2020–21 Premier League debut in the first match of the season against Liverpool on 12 September 2020, starting in the 3–4 defeat at Anfield to the reigning champions.

[33] Meslier conceded 22 goals in seven games during the month of April 2023, during which time the team took just four points from a possible 21 and resulted in the dismissal of Head Coach Javi Gracia.