The Gunners' longest-serving player stressed he is leaving with a "heavy heart" following "11 incredible years".
The Wales midfielder, 28, will become the world's eighth-best paid player when he moves to the Serie A champions in a £400,000-a-week, four-year deal.
Ramsey posted on Instagram: "As you may have already heard. I have agreed a pre-contract agreement with Juventus.
"I wanted to leave a personal statement for all the Arsenal fans who have been extremely loyal and supportive.
"You welcomed me as a teenager and have been there for me though all the highs and lows I've encountered during my time at the club.
"It is with a heavy heart that I leave after 11 incredible years in North London. Thank you."
With Arsenal in fifth spot, level with Chelsea and a point behind Manchester United, Ramsey insists he is still fired up for helping them qualify for the Champions League.
He added: "I will continue to give the team 100% and hope to finish the season strongly, before heading on to my next chapter in Turin."
Gunners supporters responded in kind to Ramsey's message.
One replied: "You're the man Aaron. Classy as ever. Best of luck in Italy, but you'll always be missed in an Arsenal shirt."
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