Coventry City will receive an initial £1.5 million fee for Thompson. but performance-related clauses in the contract mean that fee could rise by a further £1million.
Thompson, who joined City from Liverpool for £3million two seasons ago, signed in time to make his Rovers debut against Middlesbrough at the weekend if selected.
Blackburn's chief executive, John Williams, said: "David is a player Graeme Souness identified some time ago and we are very pleased to have brought him on board ahead of Saturday's deadline."