Martin Andresen was a regular on many Norwegian national youth teams while playing for Moss, Viking and Stabæk Fotball from 1995–1999. After the 1999 season, Andresen was sold to Premier League club Wimbledon in a deal worth £1,8 million. But like many of the other Norwegians in the club, his stay became short and unsuccessful. After a short loan spell at Molde, Andresen returned to his motherclub Stabæk in 2001, where he proved himself to be one of the best central midfielders in Norway.
After a brilliant 2003 season, where Stabæk captured the bronze medals in the Norwegian Premier League, Andresen was loaned out to the Premiership club Blackburn Rovers from February–August 2004, but did not sign a longer deal with the English club. Andresen once again decided to return to Stabæk to save the club from relegation from the Norwegian Premier League, but despite that Andresen played even while injured, Stabæk could not save their spot in the highest Norwegian league. Andresen, not willing to play in the Adeccoliga, asked to be sold. Many clubs in Norway were interested in the newly appointed national team captain, but the high price scared many away, including the champions Rosenborg. Vålerenga looked set to capture Andresen just before Christmas 2004, but Brann, with help from local investors signed the midfielder on 23 December 2004.
Martin Andresen became the most expensive transfer in Brann history, in a deal worth ca. 15.000.000 NOK (£1.310.000). After a disappointing first season, much ruined by injuries, Andresen made it clear that he would be "fit for fight" in 2006. In the pre-season he was appointed captain for Brann, clearly showing his importance for the club on and off the field. In 2006, Brann had their best season opening ever, with Andresen filling the captain role. He also periodically captained the Norwegian national team, playing in central midfield. In 2007 Brann won the Norwegian League, with Andresen as captain. He was described as the most valuable player by many Norwegian pundits.[who?] He was also named in the Team of the Year.
Andresen was announced as the new manager of Vålerenga on 6 November 2007 while still under contract with Brann for the remainder of the year. Brann terminated their working relationship with Andresen the day after. He signed a three-year-long contract with Vålerenga as player and manager. Andresen became the first player/head coach in the Norwegian top division (Tippeligaen) since Kjetil Rekdal (also with Vålerenga) in 2002.
He retired as a player before the 2010 season, but continued to play several matches for the reserve team in the Norwegian Second Division. In 2011 he is going to play for Follo FK in the same division when he can find the time.
On 15 October 2012, Andresen was dismissed as manager for Vålerenga.
He decided to do a come-back as a player, and joined Stabæk, who had been relegated from Tippeligaen, ahead of the 2013 season.