Mkhitaryan started the season as arguably United's best player, with one goal and five assists being registered during the opening month of the campaign.
However, the Armenian playmaker has spent the majority of the last two months on the sidelines and when United registered an interest in Sanchez, the Gunners requested that they be allowed to open talks with Mkhitaryan.
While United quickly agreed terms with Sanchez, Mkhitaryan's representative Mino Raiola indicated that the 29-year-old was not guaranteed to move in the opposite direction, despite reports suggesting that the completion of the transfer hinged on Mkhitaryan.
The former Borussia Dortmund man still had two-and-a-half years remaining on his contract at United, but the player eventually agreed to a fresh start at the Emirates Stadium.
Arsenal have not disclosed the length of Mkhitaryan's contract, but it has been described as "a long-term" deal.