Jensen is an educated economist and holds a master's degree in economics from Aalborg University which he received in 1986.

[2] When Mogens Lykketoft resigned as leader of the Social Democrats after losing the 2005 Danish parliamentary election, Jensen and Helle Thorning-Schmidt were the two candidates to succeed him.

In 2009 he was elected as the Social Democrats lead candidate for Lord Mayor of Copenhagen.

[4] In 2011, Jensen was accused of trying to lick a female coworker at a julefrokost at the Copenhagen City Hall.

[6] On 19 October 2020, Jensen announced he would stop in politics and step down as Lord Mayor and Deputy Leader as a result of the allegations.