Manager Kean, who took over from former boss Sam Allardyce in December, said: "John has a wealth of experience, both here and abroad, and he is very much focused on the development of players.
"His views and philosophies on football dovetail with mine and he has also shown himself to be a very loyal assistant, a massively important factor for me. I am delighted to welcome him aboard."
Although he was jovially mocked by Arsenal fans for his lack of goals, he was a key part of the Gunners side that won the FA Cup and League Cup in his first season at the club in 1992-93 and the European Cup Winners' Cup a year later.
After leaving London Jensen became a player-manager at Danish team Herfolge BK where he led the club to the Danish Superliga title for the first time in their history.
His most recent job before moving to Ewood Park was as manager of Danish side Randers.
Jensen becomes the first appointment at Blackburn since the club was taken over by new owners Venky's in November.
Meanwhile, promising young striker Nick Blackman has signed a new two-and-a-half year deal keeping him at the club until 2013.
The 21-year-old returned to the club this month after a successful loan spell at Motherwell where he scored 10 goals in 18 appearances.
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