It had looked like Sánchez was destined for Manchester City as they swooped for him in summer, before agreeing a deal in principle to bring him on-board during the Janaury window.
However, United gazumped City financially once negotiations began this month, eventually settling on a deal that involves Mkhitaryan going the other way rather than the £35 million fee the Gunners originally demanded.
Sánchez's agent will take a huge chunk for negotiating the deal, around £10 million. It's thought that his client will earn around £400,000 per week.
A catalyst for a title push?
Despite the hit to their bank balance, the news comes as a huge boost to United, 12 points behind City in the league, as they try to catch up to their rivals over the remainder of the season.
Sánchez won't be cup-tied for the Champions League either, meaning he's available to face Sevilla in the last 16 next month.
He leaves Arsenal after four years, two FA Cup wins and 80 goals.
The issue for Jose Mourinho's men has been against their fellow top four sides.
They put three past Arsenal at the Emirates, but drew blanks away to Liverpool and Chelsea, while only managing a solitary goal in games against Tottenham Hotspur and table-topping City. They'll be hoping that their new signing can help solve that issue.
Sánchez could make his debut against Yeovil Town in the FA Cup on Friday, with his first league appearance for United likely to be against Spurs a week on Wednesday.