The 28-year-old Wales international will arrive in northern Italy on July 1 with his contract running until June 30, 2023.
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 began his career at Cardiff City, making his his first team debut in 2007 before arriving at Arsenal in July 2008.
Over the past decade he has played 256 Premier League games, scoring 38 top-flight goals, and winning three FA Cup and two Community Shield.
He also had two loan spells at Nottingham Forest in 2010, and back at former club, Cardiff in 2011.
"As well as being recognised as a solid Premier League player, Ramsey brings a wealth of European experience," Juventus said.
Ramsey has 58 caps for Wales, scoring 14 goals, and was a part of the Welsh side that reached the Euro 2016 semi-finals.
He becomes the third Welshman to play for Juventus following club legend John Charles and former European Golden Boot winner Ian Rush.