Rantanen made his professional hockey debut with TPS Turku of Liiga, the top league in Finland, at age 16 and had three points (two goals, assist) in 15 games. The following season, the alternate captain became the only 17-year-old to play his third season with TPS and had 28 points (nine goals, 19 assists) in 56 games.

During Rantanen's NHL Draft-eligible year, he was rated as the top European skater at the end of the 2014-15 season by NHL Central Scouting and was chosen by the Colorado Avalanche with the No. 10 pick of the 2015 NHL Draft. Rantanen played 52 games for San Antonio of the American Hockey League in 2015-16 and shared the Dudley (Red) Garrett Memorial Award, given to the league's outstanding rookie, with Providence forward Frank Vatrano. He led San Antonio that season with 60 points (also the most among AHL rookies), 24 goals, 36 assists and a plus-20 rating. He was the seventh teenager in league history to reach that mark.

With five points (two goals, three assists) in seven games, Rantanen helped Finland win a gold medal at the 2016 IIHF World Junior Championship. He made his NHL debut for the Avalanche on Oct. 8, 2015, against the Minnesota Wild in Denver, and played nine NHL games in 2015-16.

He got his first NHL point Nov. 5, 2016, with an assist against the Wild at home, and scored his first NHL goal six days later, also at home, against the Winnipeg Jets. Rantanen led the Avalanche in 2016-17 with 20 goals as a rookie.