Landeskog began his youth career in hockey playing for Hammarby IF. After a successful season for Djurgårdens IF in the J20 SuperElit, Landeskog debuted in Elitserien on 21 February 2009, in a game against Brynäs IF, which Djurgården lost 2–4. At age 16 years and 90 days he became the youngest player in Djurgården’s history, and one of the youngest to ever have played in Elitserien. He recorded his first point in Elitserien on 24 February in his second game, a 2–2 tie against Skellefteå AIK.

Landeskog was initially drafted in the first round, third overall, by the Plymouth Whalers of the Ontario Hockey League in the 2009 Canadian Hockey League Import Draft. On 4 August 2009, his CHL rights were traded from the Whalers to the Kitchener Rangers.

In December 2009 Landeskog was left off Sweden’s roster for the 2010 World Junior Championships.

On 24 October 2010 Landeskog was named captain of the Kitchener Rangers for the 2010–11 season. This announcement made him the first European captain in franchise history. During his final season before NHL draft eligibility, despite suffering an ankle injury which shortened his campaign to 53 regular season games, he led all Rangers with 37 goals and a Plus-minus of 27. During the playoffs, Landeskog posted a team high 10 points in a seven series first round defeat to the Plymouth Whalers to end his Junior career.

Landeskog was drafted 2nd overall by the Colorado Avalanche in the 2011 NHL Entry Draft. He is tied with Daniel Sedin of the Vancouver Canucks and Victor Hedman of the Tampa Bay Lightning as the second highest Swedish draft pick in history – Mats Sundin and Rasmus Dahlin are the only Swedish players to be selected first overall in the draft. Landeskog became the first Swedish-born player ever drafted in the first-round out of the Ontario Hockey League (Rickard Rakell would be selected 30th overall in the same draft). Subsequently, the Kitchener Rangers dropped him from their roster to free up a position on their roster on the anticipation he would be playing in the NHL the next year. He made the Avalanche roster for the 2011–12 season; one factor in this decision was possibly that it enabled the team to reach the floor value for the salary cap.

Landeskog scored his first National Hockey League goal on 12 October 2011 against Steve Mason of the Columbus Blue Jackets on a deflection of a Jan Hejda shot with 41 seconds left in the game to send the game into overtime. At 18 years, 324 days, he was the youngest Swedish born hockey player to score an NHL goal. Since, Carolina Hurricanes Forward, Elias Lindholm broke Landeskog’s record by scoring his first NHL Goal at 18 years and 311 days. Landeskog was the first rookie to score his first NHL goal as an equalizer in the final minute of the third period since Tom Gilbert of the Edmonton Oilers did it in 2007. On 22 October 2011, he compiled his first two-goal NHL game in a 5–4 shootout victory against the Chicago Blackhawks. Landeskog’s second goal tied the game with 1:48 left to go in the 3rd period, sending the game into overtime and an eventual shootout. Landeskog recorded his first five-minute major for fighting, against newly acquired opponent Jack Johnson of the Columbus Blue Jackets on 1 March 2012. On 1 March 2012, Landeskog was named NHL’s Top Rookie for the month of February after scoring seven goals and recording six assists for the month.

On 4 September 2012, the Colorado Avalanche announced Landeskog as team captain, at the time making him the youngest captain in NHL history. At 19 years and 286 days (or 19 years, nine months and 13 days), Landeskog was 11 days younger than when Sidney Crosby was named captain of the Pittsburgh Penguins. On 5 October 2016, Connor McDavid of the Edmonton Oilers became the youngest captain in league history surpassing Landeskog’s mark by 20 days. However, because of the NHL lockout, he wouldn’t be able to play a game as captain until 19 January 2013. When the 2012–13 NHL lockout was in effect, Landeskog returned to Sweden to begin the season with Djurgården, who were relegated the previous season from the Elitserien to the HockeyAllsvenskan. In 17 games with the mid-table Djurgården, Landeskog produced 6 goals for 14 points before returning to North America citing income tax issues on 3 December 2012. He trained with his former junior team, the Kitchener Rangers before an agreement was reached to end the lockout.

Landeskog played in the 2012 World Championships and was named an alternate captain for that tournament (Daniel Alfredsson was named captain). Gabriel was Sweden’s second youngest player participating at the tournament, about eight months older than Jonas Brodin. Upon the conclusion of his second consecutive season with the Avalanche out of the playoffs, Landeskog was added to the Swedish squad for the 2013 World Championships. In 10 games, Landeskog contributed with 3 goals and 4 points in helping Sweden claim the Gold over Switzerland, becoming the first host team in 27 years to do so.

In July 2013 Landeskog was one of 35 players invited to the Swedish Ice Hockey Federation’s Orientation Camp for the 2014 Winter Olympics in Sochi. He was later included in the final squad and helped Sweden claim a Silver medal in a 3–0 defeat to defending champions Canada.

Landeskog proved to be a significant piece of a resurgent Colorado Avalanche team during the 2013–14 season. He put up career highs in goals, assists, and points, helping the Avs to a division title. He scored his first career NHL playoff goal on 17 April 2014, against Ilya Bryzgalov of the Minnesota Wild.

Landeskog recorded his first career hat trick in a 6–2 win over the Washington Capitals on 17 November 2017. He recorded his second career hat trick the following month in a 6–5 loss to the Tampa Bay Lightning. The Avalanche qualified for the 2018 Stanley Cup playoffs but lost to the Predators in six games.

Landeskog recorded his third career hat trick in a 5–3 win over the New Jersey Devils on 18 October 2018. Landeskog ended the week leading the NHL in goals and was selected as the NHL’s first Star of the Week. He was later one of three Avalanche players who were selected to participate in the 2019 NHL All-Star Game. It was the first NHL All-Star Game of his career.

He married his fiancé Melissa Shouldice on 7 July 2018 and their daughter, Linnea Rae was born 1st November 2019.