The Gunners' interest in the 26-year-old was first revealed in late June, and an agreement has now been reached between the two parties. Meslier and his representatives were at the training centre to complete the paperwork and undergo a medical, with the move expected to be confirmed imminently, reports the BBC Sport.
The Frenchman has fallen down the pecking order at Elland Road after five years as first-choice goalkeeper, and is available on a free transfer having entered the final months of his contract this summer without a renewal being agreed.
He made over 200 appearances for Leeds United after arriving from Lorient in 2020, establishing himself as a regular during their promotion campaigns, but did not feature at all for the first team last season, unable to displace either Lucas Perri or Karl Darlow after losing his place under Daniel Farke.
Meslier's departure brings the curtain down on a six-and-a-half-year association with Leeds that began when he broke into the side as a teenager. He played a significant role in two Championship title-winning seasons for the Yorkshire club, but his form dipped during the 2024-25 campaign, and he has been unable to force his way back into contention since.
Arsenal's move for Meslier comes amid uncertainty over the future of current second-choice goalkeeper Kepa Arrizabalaga, whose long-term role at the Emirates Stadium is unclear heading into the new season. That uncertainty has prompted the Gunners to explore the goalkeeping market for a potential replacement, even as they continue to build around first-choice David Raya.
As things stand, Meslier will slot in as Arsenal's third-choice goalkeeper behind Raya and Kepa. Should Kepa depart before the window closes, however, Meslier would be in line for a promotion to the number two role.
His imminent arrival is also set to have a knock-on effect further down Arsenal's goalkeeping ranks, with teenage stopper Tommy Setford now expected to leave the club on loan for the season to continue his development elsewhere, having found regular first-team opportunities hard to come by at the Emirates.
Arsenal are reigning Premier League champions and will be keen to have their goalkeeping department settled before the new campaign gets under way, with Meslier's experience of English football viewed as a useful asset even in a squad role.