The 43-year-old was promoted from first-team coach to caretaker boss following the surprise sacking of Sam Allardyce and assistant Neil McDonald last week.
New owners Venky's stressed they would not be rushing to appoint a permanent successor to Allardyce, and on Wednesday they put their trust in Kean despite his lack of managerial experience.
A club statement read: "Following the departure of Mr Sam Allardyce as football manager of Blackburn Rovers Football Club earlier this month, Mr Steve Kean was appointed as manager.
"Venky's London Limited - Blackburn Rovers - has decided to continue with Mr Steve Kean as manager, until the end of the season, June 2011."
Source: PA
Source: PA