Following his successful campaign, Bäckström was drafted fourth overall by the Washington Capitals at the 2006 NHL Entry Draft, but announced on 10 July 2006, that he would wait a year before leaving Sweden to play in the NHL. His selection made him the fourth-highest drafted Swede at the time, after Mats Sundin (first), Daniel Sedin (second) and Henrik Sedin (third).

Bäckström played his first game with Sweden on 6 April 2006, in a game against Norway. He won the World Championship when he represented Sweden in the 2006 World Championship. As of that tournament, he is the youngest Swedish player ever in an Ice Hockey World Championship tournament. Bäckström played the last four games in the World Championship (roster spot held open for Daniel Alfredsson) and was directly appointed to the first line together with idols Henrik Zetterberg and Johan Franzén.

On 21 May 2007, Bäckström signed a three-year, entry-level contract with the Capitals to begin playing during the 2007–08 season. His development and impressive play led some, such as HockeysFuture.com, which ranks NHL prospects, to consider him the most talented Swedish prospect in recent history. Drawing comparisons to Peter Forsberg, he was noted primarily for his vision, passing and ability to maintain possession of the puck in traffic. For these reasons, he was expected to be a catalyst on the team’s power play, and his defensive prowess and puck movement would make him an equally valuable asset when short-handed. On 5 October 2007, he scored his first NHL point, an assist on a goal by fellow Swede Michael Nylander, against the Atlanta Thrashers. While Bäckström was decent early in his first season, still adjusting to the smaller ice rinks of North America, his season rapidly improved once an injury to centre Michael Nylander promoted him to Washington’s first line. Playing alongside Alexander Ovechkin, Bäckström set NHL and team records while helping Ovechkin win the Art Ross Trophy and the Maurice “Rocket” Richard Trophy.

Following the 2009 playoffs, Bäckström was awarded the Viking Award as the top Swedish-born player during the 2008–09 season. He became only the second Capital to ever win the award, following Calle Johansson, who won the award in 1991–92.

Bäckström led Sweden in the 2010 Winter Olympics with six points in four games before they were eliminated by Slovakia in the quarterfinals.

On 17 April 2012, Bäckström received a one-game suspension for a cross-check to the head of Boston Bruins forward Rich Peverley.

During the 2012–13 NHL lockout, Bäckström played for Dynamo Moscow of the Kontinental Hockey League (KHL). On 18 October 2012, he signed with the Russian club, with whom his linemate Alexander Ovechkin had also signed for, for the duration of the 2012–13 lockout. Bäckström later returned to finish third in the NHL with 40 assists during the shortened 2012–13 season.

During the 2014–15 season, on 13 December 2014, Bäckström scored his first regular season NHL hat-trick in a game against the Tampa Bay Lightning. On 15 March 2015, in a game against the Boston Bruins, he became the Capitals’ all-time franchise leader in assists, surpassing both Alexander Ovechkin and Michal Pivoňka after recording two in the game. Bäckström finished the season leading the NHL with 60 assists, including 33 on Ovechkin’s League-leading 53 goals; Bäckström also finished the year with 78 points, sixth-best in the NHL. On 27 May, Bäckström had successful arthroscopic hip surgery, with Capitals management expectant of a full recovery prior to the beginning of the 2015–16 season, during which he recorded 20 goals and 50 assists as the Capitals were the best team overall during the regular season, and was selected for his first All-Star Game.

In a drug test at the 2014 Winter Olympics, Bäckström’s A-sample indicated doping due to an allergy medication containing pseudoephedrine. He was prevented from playing in the final as a result. The B-sample, analyzed after the final, also showed values above the allowed limit. The International Ice Hockey Federation (IIHF) opposed the decision to stop Bäckström from playing in the final. His silver medal was withheld until the International Olympic Committee (IOC) determined whether or not to award it to him. On 14 March 2014, the IOC Disciplinary Commission decided that Bäckström would be awarded the silver medal. The Commission confirmed the provisional suspension that rendered Bäckström ineligible for the final. However, in November 2014, the World Anti-Doping Agency (WADA) appealed the IOC decision to award Bäckström his silver medal. This appeal was resolved in January 2015 when Bäckström, the IOC, WADA and the IIHF agreed to a settlement in which he accepted a reprimand but was cleared of attempting to enhance his performance.

Bäckström reached and surpassed 600 assists in a 23 October 2018 game against the Vancouver Canucks, and became the 87th player in NHL history to reach this mark. A pre-game ceremony was held for Bäckström for reaching 600 career assists on 7 November 2018, before the Capitals’ game against the Pittsburgh Penguins. In a 4–1 win against the New York Islanders on 26 November, Bäckström recorded three assists and moved to the second place on the Capitals’ all-time points list, passing Peter Bondra. In his next game, on 30 November, versus the New Jersey Devils, Bäckström scored his second career regular season hat-trick. On 11 December, Bäckström had his 12th career four-assist game in a 6–2 win over the Detroit Red Wings, tying him with Gilbert Perreault for eighth in NHL history.

On 14 January 2020, the Capitals signed Bäckström to a five-year, $46 million contract extension.