Mkhitaryan joined Roma at the start of last season after a disappointing 18-month spell at Arsenal following a swap deal in January 2018 which saw Chilean forward Alexis Sanchez move to Manchester United.
Roma had initially reached an agreement last month to extend Mkhitaryan's loan deal until the end of next season.
"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," Arsenal said in a statement.
Mkhitaryan scored nine goals and grabbed six assists last season as Roma finished fifth in Serie A to qualify for the Europa League.
The new Serie A season begins on Sept. 19.