He joined Burnley in 2003 and played more than 300 games in all competitions, helping the club win promotion to the top-flight Premier League in 2009.

Born and raised in the Nørrebro quarter of Copenhagen, Jensen began playing football as a defender in the youth team of B 93.

[2] Jensen managed one appearance in the Eredivisie championship in his time at Alkmaar,[4] serving exclusively as a substitute for Dutch international keeper Oscar Moens.

[3] While waiting for his Alkmaar contract to run out, Jensen trained with Division One side West Bromwich Albion, where his imposing stature earned him the nickname "The Beast".

He helped the club survive in Division One in 1999–2000, and was a regular for much of the following season, until the arrival of Russell Hoult saw the end of Jensen's playing time for WBA in February 2001.

[10] After a run of performances in which Jensen's form was found lacking by Burnley manager Steve Cotterill, goalkeeper Mike Pollitt was brought on loan to Turf Moor in January 2007.

[13] Burnley brought in another goalkeeper, Gábor Király, before the 2007–08 season and Jensen found himself once again seemingly second choice, spending four months out of the team from mid-September.

On 24 June 2015, Jensen signed a one-year deal[28] with League Two rivals Mansfield Town on a free transfer as a player and goalkeeping coach.

[31] After a playing career spanning over 25 years, Jensen launched a new GK Icon youth goalkeeping academy in Sandbach, Cheshire on 31 May 2016.

[32] On 1 June 2018, it was announced that he had returned to Bury on a two-year contract as the first team goalkeeping coach, working with manager Ryan Lowe.

[34] Brian is the father of goalkeeper Sebastian Jensen who currently plays for Premier League side Brighton and Hove Albion in their U21 team.