David Moyes said: "Juan is one of the finest playmakers in the game today and it's a real pleasure to have secured his signature. He's been instrumental in Chelsea's recent success, with a notable 28 assists and 32 goals in his last two Premier League seasons.
"I have been impressed with the excitement he has shown to be part of the new Manchester United. I know our fans have admired Juan for some time now – he has always played well against us – and I know they will be delighted to see him in the red of United, starting on Tuesday."