The Wales worldwide has agreed a four-year deal and will officially join the Italian champions in July.
Ramsey had been in talks with Arsenal over new terms until the club withdrew their offer in October, leaving Ramsey free to end his 11-year spell at the club where he played 259 times and scored 61 goals.
Juventus said that the club are liable to pay 3.7 million euros ($4.1 million) by July 10 in the absence of a transfer fee.
Ramsey signed for Arsenal from Cardiff City in the summer of 2008 and despite having faced hardships in the initial parts of his career with the Gunners owing to injuries, the Wales global had grown into an integral part of the team in recent years.
He becomes the third Welshman to play for Juventus following club legend John Charles and former European Golden Boot victor Ian Rush.
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"I wanted to issue a personal statement for all the Arsenal fans wh have been extremely loyal and supportive".
According to a BBC report, Ramsey will earn over £400,000 a week, making him the highest-earning British player ever based on basic salary.
"I will continue to give the team 100% and hope to finish the season strongly, before heading onto my next chapter in Turin".
Ramsey won three FA Cup trophies during his 11 seasons at Arsenal. 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", it read.