The Armenian is set to have his medical on Sunday and Monday after the paperwork for his transfer was completed on Saturday.
This comes after it had emerged that both players had said their goodbye's to their respective team-mates earlier today.
It is not clear what the length of
Mkhitaryan's contract or his salary with the Gunners will be.
Arsenal manager Arsene Wenger had said striker Sanchez, 29, would only join United if Mkhitaryan moved to Arsenal earlier this week.
The Chilean missed Arsenal's splendid 4-1 win over Crystal Palace on Saturday because he was travelling to Manchester.
"He didn't play because you cannot drive up north and play football at the same time,"
United boss Jose Mourinho, meanwhile, said a deal to sign Sanchez was "close" following
his side's 1-0 win at Burnley on Saturday.
The Red Devils beat Arsenal to the 28-year- old's signature when he signed for the Old Trafford club for £26.3m from Borussia Dortmund in July 2016.
Meanwhile, Sanchez was set to move to United's rivals Manchester City but turned
down the chance to sign for the Premier League leaders.