The 28-year-old has agreed a four-year contract that will see him join the Italian champions as a free agent, ending his 11-year spell with Arsenal.
Ramsey passed a two-part medical in January, having picked Juve following talks with a host of European clubs.
He will be the highest-earning British player ever based on basic salary.
The Wales international's Arsenal contract expires on 30 June and the Gunners will receive no fee when he leaves.
In confirming the deal, Juventus said the club would incur costs of 3.7m euros (£3.2m) but did not specify what the fee was for.
The Juventus website welcomed Ramsey by stating he will become the third Welshman to represent the club, following the John Charles and Ian Rush.
Ramsey, who joined Arsenal from Cardiff City in 2008 for a fee of around £4.8m, held preliminary talks with Barcelona and also received an offer from Paris St-Germain.
Bayern Munich, Inter Milan and Real Madrid also showed interest, with Real forward Gareth Bale understood to have encouraged his Wales team-mate to link up with him in Spain.
Arsenal did present Ramsey with the offer of a new deal in September but it was turned down and the club were not prepared to meet his salary demands.
Head coach Unai Emery had reservations about Ramsey's role in his squad.
Ramsey's desire to play as a number eight, running on to the ball from an advanced central midfield position, clashed with Emery's vision.
Emery does not usually deploy a number eight, meaning the Welshman has mainly been used in a strict deeper role without license to roam or in the number 10 position with his back to goal.
Ramsey has played 259 times for Arsenal, scoring 61 times.
In his 11 seasons at the club, he has struck double figures in a season three times, with a best mark of 16 in all competitions in 2013-14.