The 28-year-old Wales global had already been told by new Arsenal manager Unai Emery that he did not feature in his plans at the Emirates and will soon bring to an end his 10-year association with the north London club.
He is in line to earn up to £140,00 a week with the Italian club, which works out at £7.2 million a season, although Cristiano Ronaldo is Juventus' highest-paid player.
He has now reportedly agreed a deal with Juventus, and the pre-contract will be signed in the coming days when his agent flies to Italy to meet the Juventus board.
Ramsey signed for Arsenal from Cardiff City for £4.8m.
Despite making clear his future lies away from the Emirates, Ramsey has continued to play a big part in Unai Emery's first season in charge of Arsenal, scoring three goals in 25 appearances.
"In the last match I was very happy with him". It's quite a steal for Juventus who won't be paying any transfer fee for Ramsey, someone who is easily worth £85 million in this inflated market for the quality he brings into any side.
But Emery insists the player is willing to give his all. "I want his behaviour and his focus to be on West Ham on Saturday".
The midfielder's contract at the Emirates is set to expire in June for the past couple of weeks he has been able to speak with foreign clubs.
And Ramsey said as much to him during Arsenal's 3-0 win over Blackpool in the FA Cup last weekend.