Ramsey will earn an eye-watering "basic" salary of £400k per week before tax in Turin, according to the BBC's David Ornstein.
As his contract will have ended, Arsenal will not be entitled to a transfer fee.
Ramsey will become the third Welshman to play for Juve, following in the footsteps of Ian Rush - who spent just one season in Italy - and John Charles, who spent five years with the club in the 1950s and 60s.More news: Indonesian cops apologise for using snake in Papua interrogation
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Welsh worldwide Ramsey has already passed a January medical at Juve, and will link up with Massimiliano Allegri's team over the summer.
Ramsey will be the highest-earning British player in history after turning down a new deal at Arsenal following the appointment of manager Unai Emery. "I wanted to issue a personal statement for all the Arsenal fans who have been extremely loyal and supportive".
Ramsey won three FA Cup trophies during his 11 seasons at Arsenal. It is with a heavy heart that I leave after 11 incredible years in north London.
Arsenal also released a statement, thanking Ramsey for his time at the club saying: "Aaron's made a fantastic contribution to our club since joining from Cardiff City in 2008".