Andersen joined the youth teams at Vejle at age 10. Seven years later, he signed his first professional contract with the club. He made his first team debut on 25 April 2011, against FC Vestsjælland in the 1st Division, the Danish second tier. Andersen started on the bench but replaced Thomas Mikkelsen in the 63rd minute in a fixture that ended with a 2-1 victory for Vejle. He slowly progressed into an important first team player during his debut season, playing 7 games and scoring twice during the spring of 2011. In July said year, at the end of the season, Andersen signed a new three-year deal with the club. During the following season, Andersen continued to develop and played 21 league games under the reign of manager Nicolai Wael. His performances at the central midfield position in Vejle soon led to interested from several clubs in the Danish Superliga. He occasionally also captained the side. Ultimately, Andersen chose to remain at Vejle through the 2012–13 season. Initially, he remained as a key player in the squad as Vejle fought at the top of the table during the first half of the season. The club however suffered from a series of disappointing results and switched manager to Kim Brink in January 2013. Andersen got dropped from the squad and saw a drastic decrease in playing time during the spring. At the end of the campaign, Vejle finished third in the table and missed out on a promotion. Subsequently, Andersen sought a move elsewhere.
On 28 May 2013, Andersen transferred to local rival Esbjerg fB on an undisclosed fee. He signed a three-year deal with the club. Initially, Andersen struggled to break into the starting lineup, but made his debut for the side as a second half sub in a 4–0 win against Nordsjælland on 22 July. Later during the same fall, on 7 November, Andersen made his continental debut in a 2013–14 UEFA Europa League group stage win against IF Elfsborg. Andersen scored his first goal for Esbjerg in a 1–0 win against Odense on 2 March 2014. During the following campaign, in 2014–15, Andersen remained as an important first team player at Esbjerg. He made 18 appearances in the league before suffering a bad anterior cruciate ligament injury in March 2015. The injury was projected to keep him sidelined for almost 10 months. Andersen, however, returned to the pitch after being sidelined for 7 months. Ultimately, he played 15 games during the 2015–16 season. Ahead of the 2016–17 season, Andersen was appointed as Esbjerg's new club captain. His proneness to injuries would, however, continue and Andersen was sidelined for five months in November following an operation in his knee. In January 2017, Andersen announced that he would leave Esbjerg at the expiration of his contract the upcoming summer. Simultaneously, the club revealed that they were trying to find a new club for Andersen. Andersen reportedly attracted interest from Danish clubs Brøndby IF and FC Midtjylland, as well as New York City FC in the Major League Soccer. After the closing of the January transfer window, Esbjerg confirmed that there had been no offers for the midfielder. Andersen made his comeback for Esbjerg on 2 April 2017, getting subbed on in the 82nd minute in a 0–0 draw against Randers FC, ultimately ending the campaign on 15 appearances, scoring twice.
Hammarby IF
On 30 June 2017, following the expiration of his contract at Esbjerg, Andersen signed a three-year deal with the Swedish club Hammarby IF in Allsvenskan. He made his competitive debut weeks later, coming on as a half time substitute in a 3–0 loss against Elfsborg. In 2018, Andersen played 26 league games for Hammarby, pairing up with Serge-Junior Martinsson Ngouali in the central midfield, as the club finished 4th in the table. His scored one goal during the year, his first competitive goal for the club, in a 1–1 away draw against Kalmar FF on 27 May. On 29 March 2019, Andersen signed a four-year contract extension with Hammarby, running until the summer of 2023. He was appointed as the new club captain of Hammarby before the start of the 2019 season.
