Ince took the Don's to promotion last season from League 2 to League 1 and leaves them on good terms.
A club statement said: "Milton Keynes Dons FC can confirm the departure of its manager Paul Ince to take up the vacant position at Blackburn Rovers."
It continued: "The Club had a tremendous season under Paul's guidance, winning promotion via the League Two title and the Johnstone's Paint Trophy at Wembley. We were aware that a number of clubs would be alerted to Paul's considerable talents and that retaining his services might prove an impossible challenge.
"After what he has achieved in his time with the Club, we cannot deny Paul the deserved opportunity to work in the greatest league in the world and we know everybody in Milton Keynes will join us in wishing him every continued success in what is certain to be a fantastic managerial career.
"The Club will now set about appointing Paul's successor as we look to build on his history-making achievements."