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.