Peters led the Hurricanes to a 137-138-53 record during his time in charge. Carolina went 36-35-11 in 2017-18 and missed the playoffs by 14 points.
The Team Canada head coach for the 2018 IIHF World Championship said the following regarding his decision to step down:
"I want to thank [owner] Tom Dundon, [CEO] Peter Karmanos and [President of Hockey Operations] Ron Francis for the trust they put in me to lead the team. I feel the incoming general manager should have the ability to hire his own head coach. I also want to thank [Gale Force Sports & Entertainment President] Don Waddell and the entire front office and PNC Arena staff. This business requires hard work and long hours, and I greatly appreciate the efforts of the many people I have worked alongside during the past four years.
"We enjoyed our time in Raleigh, and my family will always feel a connection to North Carolina. I feel like this is a good time to move on, and I am looking forward to my next challenge."
The Hurricanes have gone nine seasons without making the playoffs, which is the NHL's longest active drought.
Carolina provided Peters with his first NHL head-coaching job after he served as an assistant with the Detroit Red Wings for three seasons.
The 53-year-old Peters previously coached the WHL's Spokane Chiefs and AHL's Rockford IceHogs.
This is Carolina's fifth coaching change since relocating from Hartford, Connecticut, in 1997. Its next head coach will be its fourth since the start of the 2011-12 season.