The former Denmark international joined Rovers in January after Kean was made the permanent manager after Sam Allardyce was sacked.
"To be asked to stay on means an awful lot to me," Jensen told the club's official website.
"Steve told me a few weeks ago that he was keen for me to stay whatever happened, but the situation is clearly much better now we have secured our Premier League status.
"It is apparent to me that the Premier League is by far and away the best competition in the world and to be able to be part of it at a club as good as this is very exciting."