Ramsey will join Juve as a free agent in a deal reportedly worth £400,000-a-week.
He wrote on Instagram: "As you may have already heard, I have agreed a pre-contract with Juventus Football Club.
"I wanted to issue 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 through 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.
"I will continue to give the team 100 per cent and hope to finish the season strongly, before heading on to my next chapter in Turin.
"Kind regards, Aaron."