Rantanen made his professional hockey debut with TPS Turku of Liiga, the top league in Finland, during the 2012-13 season and had three points (two goals, one assist) in 15 games as a 16-year-old forward. He entered 2014-15 as the only 17-year-old to play his third season with TPS and finished with 28 points (nine goals, 19 assists) in 56 games while serving as an alternate captain.

NHL Central Scouting rated Rantanen as the top European skater available in the 2015 NHL Draft, and he was chosen by the Colorado Avalanche in the first round (No. 10). He opened the 2015-16 season with Colorado and made his NHL debut on Oct. 8, 2015, but was sent to San Antonio of the American Hockey League after two weeks. Rantanen had a goal and an assist in his AHL debut and went on to share the Dudley (Red) Garrett Memorial Award, given to the league's outstanding rookie, with Providence forward Frank Vatrano. Rantanen led all AHL rookies in scoring with 60 points (24 goals, 36 assists) and a plus-20 rating in 52 games.

With five points (two goals, three assists) in seven games, Rantanen also helped Finland win a gold medal at the 2016 IIHF World Junior Championship.

Rantanen made the Avalanche for good in 2016-17. He had an assist against the Minnesota Wild on Nov. 5, 2016, scored his first NHL goal six days later against the Winnipeg Jets and finished with 20 goals in 75 games to lead the last-place Avalanche.

The Avalanche rebounded to make the Stanley Cup Playoffs in 2017-18, and Rantanen's improvement was a big reason. He finished with 84 points (29 goals, 55 assists) in 81 games, finishing second on the team in scoring behind linemate Nathan MacKinnon (97 points).

Four seasons later, Rantanen set what were NHL career highs in goals (36), assists (56) and points (92) in 75 regular-season games. He won the Stanley Cup after getting 25 points (five goals, 20 assists) in 20 playoff games, eight assists coming against the Tampa Bay Lightning in the Stanley Cup Final that was one shy of the official NHL record in the Final by Daniel Briere with the 2010 Philadelphia Flyers, Larry Murphy with the 1991 Pittsburgh Penguins, Wayne Gretzky with the 1987 Edmonton Oilers and Jacques Lemaire with the 1973 Montreal Canadiens.

In the 2022-23 season, Rantanen scored 55 goals, tied for third-most in Avalanche/Quebec Nordiques history (Michel Goulet scored 55 goals with the Nordiques in 1984-85, 56 in 1983-84, and 57 in 1982-83).

Rantanen was named to Finland's roster for the 4 Nations Face-Off during the 2024-25 season. After playing 10 seasons with Colorado, he was acquired by the Carolina Hurricanes on Jan. 24, 2025, in a three-team trade also involving the Chicago Blackhawks for forwards Jack Drury and Martin Necas, a second-round pick in the 2025 NHL Draft and a fourth-round pick in the 2026 NHL Draft. He was then traded to the Dallas Stars on March 7, 2025, for Logan Stankoven and a first-round and third-round pick in the 2026 NHL Draft, a first and third in the 2027 NHL Draft and a first-round pick in the 2028 NHL Draft.

Rantanen then signed an eight-year, $96 million contract with the Stars. He helped eliminate the Avalanche from the Western Conference First Round with a hat trick and an assist in the third period, when Dallas scored four unanswered goals in a 4-2 win in Game 7 at American Airlines Center. He became the first player in NHL history to score a hat trick in the third period of a Game 7, and the first with multiple four-point periods in a single postseason after also achieving the feat with a goal and three assists in the second period of Game 6.

Rantanen had two goals and an assist in a 4-3 shootout win against the Edmonton Oilers in Dallas on Nov. 4, 2025, to become the fourth Finland-born player to score at least 300 goals in the NHL, joining Teemu Selanne (684), Jari Kurri (601) and Olli Jokinen (321). He was named to Team Finland's roster for the Olympic Winter Games Milano Cortina 2026.