The 21-year-old had an impressive season with the Whites last year and the Premier League side have offered him a new five-year contract.
Meslier has managed to establish himself as the first-choice shot-stopper at Elland Road after displacing Kiko Casilla in the starting line-up and he will be hoping to push on and continue his development with the Whites next season.
The French under 21 international is highly rated at the Premier League club and he has a big future ahead of him.
Leeds paid a fee of around £5 million to sign the goalkeeper last summer from Lorient and he has the potential to develop into a top-class player for them in future.
Marcelo Bielsa will be hoping to keep his squad intact going into the new season and the new deal for Meslier was a no brainer.
The 21-year-old will be hoping to build on his performances from last season and establish himself as a reliable Premier League goalkeeper in the coming months.
Last season he was the youngest goalkeeper in Europe’s top five leagues to make more than ten starts and he managed to keep eleven Premier League clean sheets which is a record for an under 21 keeper.
“I’m so proud,” said Meslier, after signing his new deal.
“I’m very happy to sign a new deal with Leeds, a big club, so it was natural to sign and I have no doubts.
“I have the chance to play in the Premier League at 21, which is not a given for everyone and I feel very happy to play every weekend against big teams.
“Last season I discovered the Premier League, I was young for a goalkeeper, so this season I have to confirm the challenge and take the opportunity the club has given me.
“I will give the maximum of myself and keep working every day with the goalkeeper coaches, it’s an important season for me and the rest of the team too.
“We work hard every day with Marcelo to try and get the best out of ourselves, we were not surprised to finish ninth last season, but we know this season will be difficult because the teams know us now, so we have to work more to try and have another good season.
“This club is unbelievable, the stadium is full all of the time and you feel the atmosphere of the fans and we play football everybody likes.
“I can’t wait to play in the Premier League with Elland Road full.”