Tolvanen began his professional career with Espoo in Finland's Jr. A league in 2014-15 before moving to North America to further his development. He scored 17 goals in 49 games with Sioux City of the United States Hockey League in 2015-16, making the USHL All-Rooke Team, and increased that total to 30 in 53 games the following season when he made the First All-Star Team.

Playing for Finland at the 2016 IIHF World Junior Championship, he had seven goals in seven games to help win the gold medal.

Tolvanen was selected by the Nashville Predators in the first round (No. 30) of the 2017 NHL Draft and played in the Kontinental Hockey League with Jokerit in 2017-18, finishing with 36 points (19 goals, 17 assists) in 49 games and seven points (six goals, one assist) in 11 playoff games. He had a hat trick in his first KHL game on Aug. 23 and was voted to the KHL All-Star Game.

After signing a three-year, entry-level contract with the Predators on March 29, 2018, Tolvanen made his NHL debut three days later. He was scoreless in three late-season games with the Predators and did not dress for any Stanley Cup Playoff games.

Tolvanen was claimed off waivers from the Predators by the Seattle Kraken on Dec. 12, 2022. He helped Team Finland win bronze at the Olympic Winter Games Milano Cortina 2026 and represented his country at the 2018 PyeongChang Olympics, where he had had nine points (three goals, six assists) and was named to the Olympic All-Star team.