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Born into a Danish family residing in Victoria, British Columbia, Jensen began his career in his home country at the age of sixteen playing jazz and classical music. He then joined Radio Luxembourg at the age of eighteen in 1968.
By 1974, Jensen was becoming a TV personality in Britain, hosting pop shows on ITV, and in the mid-1970s he worked for the then-new Radio Trent (now Capital East Midlands) in Nottingham, one of the first legal, land-based commercial radio stations in the UK. During the early part of his career he was billed as "Kid Jensen" and did not use his given name professionally until 1980.
BBC Radio 1
In 1976 he joined the BBC's pop network, Radio 1, initially hosting a Saturday morning show from 10am-midday, but sitting in for many other DJs, and eventually graduating to a weekday late afternoon/early evening show in the spring of 1978 from 4:30 to 7:00 pm. He kept his profile high through regular appearances presenting Top of the Pops, and championed many acts who went on to achieve huge commercial success, notably The Police and Gary Numan.
In September 1980, Jensen left Radio 1 to work for the then-new CNN in Atlanta, but he returned a year later, presenting the weekday evening show from 8-10pm (later extended to run from 7-10 pm). Soon afterwards he dropped the "Kid" name, although he would still be popularly known by it for many years to come. His mid-evening show was dominated by indie-rock, but also featured interviews with mainstream acts such as Duran Duran, and was the first show to champion Frankie Goes to Hollywood, before their commercial success. He remained a regular Top of the Pops presenter and struck up a famous partnership with John Peel.
In 1984, Jensen quit Radio 1 and joined London's Capital FM, presenting a weekday mid-morning show; moving to weekday drivetime in 1987. In addition to his weekday shows he also presented the weekly The Network Chart Show, the UK's first syndicated commercial radio show which originally went out every Sunday between 5pm and 7pm, competing directly with Radio 1's Top 40 show.
While presenting the Network Chart, Jensen became ITV's unofficial "face" of pop music, presenting pop shows such as "The Roxy" (an attempt to compete with Top of the Pops). He continued to comment regularly on pop-related stories in ITN and Sky News bulletins for some time after he left the Network Chart in 1993, when he was replaced by Neil Fox . Jensen continued to present the weekday drivetime show on Capital FM until 1998.
He also presented various children's programmes including Worldwise and Popquest.
In 1998, Jensen joined rival London FM station, Heart 106.2, presenting the weekday drivetime show from 4-7pm. He also presented a Sunday afternoon CD chart show called Kid Jensen's CD Countdown which was produced by Blue Revolution and networked on Birmingham's 100.7 Heart FM and various other stations.
In 2002, Jensen returned to Capital and was heard on its oldies service Capital Gold. First presenting the Monday–Thursday late night show from 10pm–1am, before taking over the weekday mid-morning slot in February 2003, then the breakfast show, (co-hosted with Erika North). Jensen later moved to the late morning slot 10am–1pm. Jensen teamed up with Capital Radio Producer Craig Kingham to present the Saturday morning show. Jensen left Gold in December 2010.
In September 2008, Jensen hosted the evening show of Planet Rock (7-11pm) as a stand-in for Nicky Horne. He also hosted Planet Rock's Sunday Morning show, "Another Dimension", and co-hosted with Rick Wakeman on Saturday mornings until December 2010 and briefly hosted the Saturday morning 10am–1pm show on his own, until he left the station in April 2011.
Jensen joined Smooth Radio in April 2011 to present an afternoon show. In April 2012, he took over the Smooth Drive Home slot (Mondays to Friday, 4pm – 8pm) from Carlos. Jensen also hosted a two-hour show on Smooth Radio on Sunday evenings. Smooth was acquired by Global Radio in 2013. Following a studio and business move to Global headquarters in Leicester Square, Jensen was dropped from the schedules on 19 December 2013. 
He was a co-presenter (off-screen) of the TV programme Gillette World Sports Special, alongside Mark Webster.
Jensen is married to wife Guðrún and they have three children and two grandchildren. Their youngest son, Viktor, a successful racing driver, both competed in and was also a National Class winner in the 2007 British and International Formula 3 Championship. Jensen also founded the Kid Jensen Racing team that briefly raced in the Formula 3000 championship, which won one race at the hands of Nicolas Minassian in 1999 at Silverstone.
In 2010 he became a Freeman of the City of London and was inducted into the UK Radio Hall of Fame.
Jensen is a fan of Crystal Palace, is chairman of the Crystal Palace F.C. Vice-President's Club, and also acted as ambassador for the CPFC 2010 consortium during the purchase of the club from administrators.
- "David "Kid" Jensen". The Radio Academy. Retrieved 23 February 2013.
- "Emma B joins Smooth Radio". Radio Today. 14 March 2011. Retrieved 27 March 2011.
- "Smooth Radio adds Donny Osmond to line-up". Radio Today. 21 March 2012. Retrieved 2 April 2012.
- "David Jensen leaves Smooth". Radio Today. 19 December 2013. Retrieved 19 December 2013.
- "Chelsea Lodge No. 3098 100 Years 1905-2005".