The 26-year-old arrives after seven years at Elland Road, where he made 215 appearances across all competitions and recorded 70 clean sheets.
Meslier began his career at FC Lorient before joining Leeds on loan in 2019, helping the club secure promotion to the Premier League.
His move was later made permanent, and he went on to make 107 top-flight appearances.
The experienced goalkeeper expressed his excitement at joining Arsenal, saying he cannot wait to win trophies with "the biggest club in England" as he strengthens Mikel Arteta’s squad.
"I’m extremely happy. It's a great day for me because I have just joined the champions. For me, Arsenal is the biggest club in England," Meslier tol Arsenal website.
"I'm very happy and very proud to join Arsenal. I cannot wait to show the love that I've got for this badge, and I cannot wait to win trophies with this team, because this is a club that needs to lift trophies again and again."