The 25-year-old Spanish midfielder completed a £37.1m move from the Blues to United on Saturday.
"I and everyone at Chelsea have massive respect for Juan and his big talent, and when he told us of his wish to move on because he wanted to play more, we did not want to deny him this opportunity," Chelsea's official website quotes him as saying.
"We want him to be successful in his career and as well as that, this transfer makes huge financial sense to us at Chelsea. We are pleased Juan will stay in England - even with a rival club. He is happy in this country and it is good the Premier League retains such a talented player.
"Juan moves with our full blessing and I can speak on behalf of everyone at the club in thanking him for his fantastic service, and wishing him well for his future."
Mata joined Chelsea from Valencia in the summer of 2011.