The Armenia international completed a move to Arsenal in a swap deal that saw Alexis Sanchez complete a switch to Manchester United.
Mkhitaryan failed to secure a regular starting spot under Red Devils boss Jose Mourinho over the past 18 months at Old Trafford.
The 29-year-old playmaker won the EFL Cup and the Europa League during his one full season at Old Trafford following a return of 13 goals in 63 games in all competitions.
The former Borussia Dortmund midfielder scored in Manchester United’s 2-0 win against Dutch giants Ajax in the Europa League final at Wembley.
Mourinho was regularly critical of the Armenian midfielder for his poor performances in the Manchester United team.
However, former Red Devils midfielder Giggs admitted that he is disappointed that Mkhitaryan didn’t work out at Old Trafford.
“I think as well as every United fan I was excited to see Henrikh Mkhitaryan join the club and he looked on the outset like a United player, scoring and creating goals,” Giggs told Sky Sports.
“I played with Juan Sebastian Veron, who was one of the most talented players on the planet, but sometimes it happens where it doesn’t work out, maybe because of injuries or maybe being played out of position.
“Maybe it will work out for him at Arsenal and he’ll set the place on fire, so I’m not sure who has got the best part of the deal, but Sanchez has scored and assisted more goals in the Premier League.”
Manchester United signed Sanchez in the swap deal after the Chile international had been regularly linked with a move to Manchester City over the past 12 months.
The Red Devils are in second place in the Premier League table but 12 point behind current leaders Manchester City.
Mkhitaryan will wear the number seven shirt at Arsenal.
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