Swedish international left back Martin Olsson joined Norwich City from Blackburn on 10th July 2013 for an undisclosed fee, thought to be around £2million. He signed a four-year deal at Carrow Road.

Olsson began his playing career in Sweden by playing for Högaborgs BK. Olsson was working his way through the youth setup at the club in 2005–06. His talent attracted the attention of football clubs in Europe, and in January 2006, English, at the time Premier League, side Blackburn Rovers signed him for their youth academy..

He made his Blackburn debut in the UEFA Cup qualifier in the 2007–08 season as a late substitution for Stephen Warnock. He made his Premier League debut against Derby County in a 2–1 victory on 30th December 2007, coming on as an 84th minute substitute for Morten Gamst Pedersen at Pride Park. He was voted Blackburn's Young Player of the Year for the season 2007–08 and in May 2008, Olsson signed a new four-year deal, keeping him at Blackburn until summer 2012. He signed a new five-year contract in the summer of 2010 in which he described as an " easy choice".

He had made 132 appearances for Blackburn at the time of his transfer to Norwich, scoring five goals.

Olsson played for Sweden's Under-18s and Under-21s before making his debut against Bosnia in May 2010, scoring twice in a 4-2 win. At the time of his transfer, he had 15 caps for Sweden and had scored four goals.

Olsson made his Norwich debut on 27th August 2013, scoring in the 6-3 Capital One Cup second round victory over Bury.

Olsson was named best Swedish defender in the Fotbollsgalan 2013 awards ceremony in Stockholm in November 2013.

He made 37 appearances, scoring once, in the 2013/14 season in which Norwich were relegated from the Premier League. As one of Norwich's "better" performers, he was linked with a move to both West Ham and West Brom at the end of the season. Norwich rejected a bid from West Ham for Olsson, with the Hammers turning instead to Ipswich's Aaron Cresswell.

In January 2015, Norwich supposedly rejected a £4m bid from Swansea for Olsson. On transfer deadline day (2nd February 2015), Olsson was clsoe to a move to West Bromwich Albion in a deal which would see Graham Dorrans join Norwich. Rumours have it that the deal collapsed when Olsson insisted on a relegation release clause.

He re-established himself in the Norwich first team and finished the season with 45 appearances and 1 goal, playing in the 2-0 Championship Play-off final victory over Middlesbrough on 25th May 2015

Olsson was part of the Sweden squad that qualified for the Euro 2016 finals, playing in the play-off win over Denmark. He was selected as part of their 23 man squad for the Euro 2016 finals in France..

He made 25 appearances for City in 2015/16, scoring once, as the Canaries were relegated from the Premier League.

Olsson impressed for Sweden in their opening gasme of the European Championships in France as they drew 1-1 with Ireland.

Olsson was linked with a move to Turkish side Besiktas. Turkish sports news agency, Sporx, reported in June 2016 that Olsson is on a watch list with Manchester City’s Aleksandar Kolarov and San Lorenzo’s Argentine left-back Emmanuel Mas. Olsson is out of contract at Carrow Road in 2017. 

Olsson transferred to Swansea on 17th January 2017 for a fee of £4million. He made his debut on 21st January 2017 in a 3-2 win over Liverpool at Anfield.

Olsson and Swansea were relegated to the Championship at the end of the 2017/18 season. Olsson was released by Swansea on 8th May 2019 to cut costs following their failure to return to the Premier League. Also departing were Wilfred Bony, Dutch winger Luciano Narsingh and Leroy Fer. Olsson made 75 appearances for Swansea, scoring twice

In January 2020 he trialled with West Brom.

On 2nd April 2020 he returned to Sweden to sign for Helsingborgs on a short term deal until the end of June 2020. “Being able to represent one’s home town where one has grown up is a nice feeling. I just want to play football and get started so the contract will not affect the club. I do this more for football. My family, friends and cousins ​​are from here so it was a pretty easy decision" said Olsson. Managed by former Aston Villa defender Olaf Mellberg, Helsingborg’s squad included former Manchester United goalkeeper Anders Lindegaard and Olsson’s twin brother Marcus who had played for Blackburn and Derby. However Martin Olsson’s 24 appearances was not enough to stop them being relegated as they finished 15th in the 16 team Allsvenskan.

On January 30th 2021 he returned to the Allsvenskan signing for BK Hacken who are based in Gothenburg. He moved on to Malmo on 12th August 2021.