Kase had 14 goals and 13 assists in 50 games with the Toronto Maple Leafs during the 2021-22 campaign.
The Czech winger, selected in the seventh round (205th overall) by the Ducks in the 2014 NHL Draft, has 57 goals and 67 assists in 257 career NHL games.
He spent nearly four full seasons in Anaheim before being traded to Boston in 2019. He sat out most of 2020-21 as he recovered from post-concussion symptoms before joining Toronto as a free agent last summer.
Toronto opted not to extend a qualifying offer to Kase earlier this week, making him an unrestricted free agent.
Kase will become a UFA at age 27 next summer at the expiration of this new deal.
Carolina GM Don Waddell pulled off a pair of big trades earlier in the day, acquiring six-time 30-goal scorer Max Pacioretty and depth defender Dylan Coghlan from the Vegas Golden Knights for future considerations.
The Hurricanes also acquired 2017 Norris Trophy winner Brent Burns at a discounted cap hit. They received Burns and forward Lane Pederson from the San Jose Sharks in exchange for forward Steven Lorentz, goalie Eetu Makiniemi and a 2023 third-round pick.