And Sanchez believes De Gea is one of the best goalkeepers in the world.
He was the top scorer in two of his three completed seasons at Emirates Stadium and helped Arsenal win the FA Cup in 2015 and '17, quickly becoming a favorite with the fans.
Reports suggest Sanchez will earn close to £500,000 (Dh2.5 million) per week at Old Trafford, including bonuses and image rights.
"He will bring his ambition, drive and personality, qualities that make a Manchester United player and a player that makes the team stronger and the supporters proud of their club dimension and prestige". And I told him that my dream was to come here to Manchester United.
Mkhitaryan was one of Mourinho's first signings in the summer of 2016 and scored 11 times in his debut season, including one goal in the Europa League final victory over Ajax.
The Armenia worldwide moved to Old Trafford from Borussia Dortmund for £26.3m in July 2016.
Arsenal made a decision to go ahead with the swap deal rather than allow the player's contract, which would have expired in June, to run down, negating the risk of losing him for nothing.More news: Neil Diamond Retires From Touring After Parkinson's Disease Diagnosis
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Arsenal boss Wenger said he was happy to acquire Mkhitaryan in the deal.
Sanchez took a swipe at his critics in an Instagram post after the deal was announced, singling out the former Arsenal players who had questioned his attitude towards the end of his stay. "Now I'm here, I'll do my best for this club to create history".
In his 19 games for Arsenal this season, Sanchez created on average 2.99 chances per 90 minutes - more than both Rashford (1.30) and Martial (2.06).
He said: "I've not had the chance to get to know them personally or spend time with any of my team-mates up to now, but of course I know them from having played against them in the past". Mkhitaryan and Sanchez visited immigration office of Liverpool, where they updated work permits in Europe. Mkhitaryan visited the same office.
The Warrington-born winger showed off his "Milly Rock" dance moves, which became famous in the States a year ago, after scoring in Manchester United's 3-1 win over Arsenal at the Emirates Stadium in December.
City considered bidding again in January but pulled out last week due to the rising costs involved.
The fee has since been cancelled out by United's willingness to trade Mkhitaryan, who was valued at the same price, in a straight-swap deal.
One of the most consistent figures in the Arsenal setup, Alexis started out with 20 goals in 44 appearances for the London outfit across competitions.