Jensen, 45, is teaming up with new boss Steve Kean, initially until the end of the season.
The former Denmark international, who has been out of work since leaving Randers in October, will make his bow against Chelsea on Saturday at Stamford Bridge.
He said: "From what I see and hear this looks like a very exciting time for Blackburn Rovers, with the new owners and a new manager.
"I think I can bring knowledge and experience to the job and I also believe I can help players become better individually and the team to improve as a collective unit. I view it as a great opportunity."
Source: PA