Ramsey will bring to a close an 11-year run with Arsenal, having been part of three FA Cup winning sides turning his time with the Gunners after moving from Cardiff City in the summer of 2008.
There was interest from various European giants, including Bayern Munich and PSG, but Ramsey's final decision was to join Juventus, where he will play alongside Miralem Pjanić and Blaise Matuidi in a midfield trio - quite the upgrade from Mateo Guendouzi and Granit Xhaka.
Ramsey, who joined Arsenal from Cardiff City in 2008, had held talks with Barcelona and Paris Saint-Germain but it became clear Turin would be his destination with terms of around £300,000-a-week being offered.
As his contract will have ended, Arsenal will not be entitled to a transfer fee.
The BBC's David Ornstein reports that Ramsey will earn £400,000 a week, making him the highest-earning British player in the world.
Welsh worldwide Ramsey has already passed a January medical at Juve, and will link up with Massimiliano Allegri's team over the summer.
Ramsey has scored 62 times and registered 64 assists in 361 appearances for Arsenal in all competitions.