A statement on Blackburn's official website read: "[As] 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.
"We are extremely happy with his contribution to our team and we wish him all the very best in his future endeavours."
Jones passed a medical in Manchester last week and has agreed a five-year contract. The deal will be completed once Jones returns from international duty with England Under-21s as they compete in the European U21 Championships in Denmark.
He made his senior debut in a Carling Cup victory at Nottingham Forest in September 2009, and went on to make 40 appearances for Blackburn.
Jones is the latest England Under-21 international to make a big-money move as Premier League clubs appear to be switching their focus away from expensive foreign imports towards home-grown talent.
Liverpool, who spent £35 million on striker Andy Carroll in January, recruited midfielder Jordan Henderson from Sunderland last week in a deal reported to be worth around £16 million.
The Anfield side were also said to be keen on signing Jones, as were North London rivals Arsenal and Tottenham Hotspur.
