Jones has signed a five-year contract with the Premier League champions.
Blackburn was forced to agree a sale after United triggered a £16.5million buyout clause in the 19-year-old’s contract.
“Manchester United is delighted to announce it has signed an agreement with Blackburn Rovers for the transfer of Phil Jones,” said a United statement.
“The player passed a medical in Manchester last week and has agreed a five-year contract.
“The deal will be completed once the player returns from international duty.”
“Much as we would love him to stay on with us, and we made all efforts to convince him to stay, Phil has to finally follow his heart,” read a statement on behalf of the owners, board and manager at Blackburn.
“We are extremely happy with his contribution to our team and we wish him all the very best in his future endeavours.”