Armenia international Mkhitaryan, 28, will have a medical on Sunday and Monday, while Chile forward Sanchez, 29, will have his on Sunday.
The length of Mkhitaryan’s contract, and his salary, is undisclosed.
Gunners boss Arsene Wenger had earlier said Sanchez would only join United if Mkhitaryan moved to Arsenal.
Sanchez missed Arsenal’s 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,” said Wenger.
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 Mkhitaryan’s signature when he signed for the Old Trafford club for £26.3m from Borussia Dortmund in July 2016.
He has made 63 appearances for United – 22 this season – scoring 13 goals.
Sanchez, meanwhile, has scored 80 goals in 166 appearances for Arsenal since joining team from Barcelona for £35m in July 2014.
The Chile international, whose contract Arsenal was due to expire in the summer, had looked set to join Manchester City last August.
It emerged this week that City had decided not to pursue their interest in signing Sanchez.
Analysis – ‘Good business for both clubs’
Former England and Newcastle striker Alan Shearer on Match of the Day
I think it is good business for both clubs.
Arsenal are getting rid of a player who doesn’t want to be there, but they are also getting a player whose face maybe didn’t fit at United, but who is much better than he’s shown at United.