The 31-year-old Armenian international spent last season on loan at Roma, where he scored nine goals in 22 Serie A appearances to help the Giallorossi finish fifth and qualify for the Europa League.
Mkhitaryan was signed for Arsenal by Arsene Wenger in January 2018 from Manchester United in a swap deal involving Alexis Sanchez but his time at the Emirates Stadium proved to be underwhelming.
Mkhitaryan made 59 appearances in all competitions for Arsenal and scored nine goals.
A statement from the Gunners read: "Micki leaves us following his season-long loan in Italy. 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.”
The former Borussia Dortmund attacker confirmed his move to the Italian capital on social media with a post that read: "I’m delighted to announce that I have permanently joined the Giallorossi."
"Firstly, I would like to thank Arsenal, its personnel and the millions of Gunners, all whom supported me over the past year and a half. A special thanks goes to Arsene Wenger for having brought me to the club and for his trust in me.
"Now the preparation begins with my new challenge and my second year adventure in Serie A.
"I love the city of Roma, I love this club and I count the fans in my heart. I will give all of my effort in helping us achieve our goals!"
