Ramsey will be out of contract at the club, where he has played since arriving in 2008.
He is set to join up with the Italian champions, where he will be one of their highest earners.
Ramsey is a fan favorite at Arsenal, but the club could not agree on terms for a new contract.
"Aaron's made a fantastic contribution to our club since joining from Cardiff City in 2008. 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.
"We look forward to Aaron helping the team to a strong end to this season before he joins Juventus in the summer."