Born in Tampere, Finland, Valimaki grew up in Nokia and was the No. 14 pick by Tri-City in the 2015 Canadian Hockey League Import Draft. The No. 16 pick by the Calgary Flames in the 2017 NHL Draft played three seasons in Tri-City and signed a three-year, entry-level contract with the Flames on July 21, 2017.
Valimaki made his NHL debut against the Vancouver Canucks on Oct. 3, 2018 and scored his first NHL goal in a 5-2 win against the Boston Bruins on Oct. 17. He was captain of Finland at the 2018 IIHF World Junior Championship and played two games for the Flames in their five-game loss to the Colorado Avalanche in the Western Conference First Round of the 2019 Stanley Cup Playoffs.