Ramsey – who has won three FA Cups at the London club – has passed a medical with the Turin club.
Aaron Ramsey signs £400,000-a-week contract with Juventus
He has not been a regular under Arsenal manager Unai Emery since he made it clear he was set to end his 11-year spell at the Emirates Stadium.
Ramsey joined Arsenal from Cardiff for £4.8m 11 years ago. He has made 259 appearances for Arsenal, and scored 61 times including a personal best of 16 goal in 2013/14.
Arsenal said in a statement that Ramsey had made a “fantastic contribution” to the club.
“He has always been a consummate professional and will always have a special place in the hearts and memories of Arsenal fans around the world,” it said.