Strålman was selected on 30 July 2005, by the Toronto Maple Leafs as their fifth draft choice, 216th overall. He was picked in the seventh and final round of the post-lockout 2005 NHL Entry Draft. Earlier the same year, on 4 April, Strålman had signed a two-year contract with Timrå IK of the Swedish Elitserien. During the following 2005–06 season, Strålman adapted to Elitserien quickly and became a team regular. On 20 January 2006, this effort was recognized when he was named the third of four candidates for the 2006 Elitserien Rookie of the Year. The award was eventually won by forwardNicklas Bäckström. On 16 May 2007, Strålman signed a three-year contract with the Toronto Maple Leafs. He made his North American professional debut on 6 October 2007, with the Toronto Marlies, the American Hockey League affiliate of the Maple Leafs, and made his NHL debut on 23 October in a home game against the Atlanta Thrashers. On 21 March 2008, he scored his first career NHL goal in a game against the Buffalo Sabres, then recorded his first multi-goal game against the Montreal Canadiens on 29 March. During the 2009 off-season, Strålman was traded twice. On 27 July, he was traded to the Calgary Flames, along with Colin Stuart and a seventh-round draft pick in 2012, in exchange for Wayne Primeau and a second-round pick in the 2011. Several months later, on 28 September, he was traded by the Flames to the Columbus Blue Jackets for a third-round pick in 2010. As a free agent after the 2010–11 season, Strålman was on a try-out contract with the New Jersey Devils, but did not stick with the team when the final team roster was released. On 3 November, he then signed a one-year contract with the New York Rangers. As a restricted free agent at the end of the season, he initially planned to bring the Rangers to a salary arbitrator, but on 26 July 2012, he signed a two-year, $3.4 million contract with New York. During the 2014 Stanley Cup playoffs, Strålman helped the Rangers reach the 2014 Stanley Cup Final, where they were ultimately defeated by the Los Angeles Kings in five games. On 1 July 2014, Strålman left the Rangers organization as an unrestricted free agent and signed a five-year, $22 million contract with the Tampa Bay Lightning. In the 2014–15 season, he set career-highs in goals, assists and points in his first season with the Lightning, helping the team reach the 2015 Stanley Cup Finals. During the 2015 Eastern Conference Finals, the Lightning defeated his former team, the Rangers, in seven games. On 27 November 2015, Strålman played in his 500th career NHL game in a 2–4 Lightning loss to the Washington Capitals. On 25 March 2016, Strålman suffered a non-displaced fracture of his left fibula, during a 7–4 win over the New York Islanders. On 21 February 2017, Strålman recorded his 200th career NHL point. Strålman's 200th point came in a 4–1 Lightning win over the visiting Edmonton Oilers at Amalie Arena. On 23 February 2017, Strålman skated in his 600th career NHL game. After five seasons with the Lightning organization, Strålman left as a free agent to sign a three-year, $16.5 million contract with the Florida Panthers on July 1, 2019.