The Armenia international spent the 2019-2020 campaign on loan with the Serie A side, scoring nine goals in 27 appearances across all competitions.
That deal was initially due to expire at the end of June but the clubs agreed a short-term extension to cover the end of the coronavirus-hit campaign.
I‘m delighted to announce that I’ve permanently joined the #giallorossi 💛❤️🐺👊🏻 I‘d like to thank @arsenal , its personnel & the millions of #gunners all whom supported me over the past 1,5Y. A special thanks to A. Wenger for having brought me to the club and for his trust in me pic.twitter.com/KD8QJuhAbT— Henrikh Mkhitaryan (@HenrikhMkh) August 31, 2020
Mkhitaryan moved to the Gunners from Manchester United in January 2018 as part of the deal that sent Alexis Sanchez in the opposite direction.
He scored nine goals in 59 appearances across all competitions before joining Roma.
A statement on the Arsenal website read: "We have agreed to terminate his contract with us by mutual consent to allow him to join Roma in a permanent move.
"Everyone at Arsenal thanks Micki for his contribution to the club and wishes him all the best for his future with Roma."