Peters has a record of 65-72-27 in two seasons while leading the Hurricanes' rebuilding project. They finished this season sixth in the Metropolitan Division with a 35-31-16 record, but earned 86 points -- their most since 2010-11, and a 15-point improvement from Peters' first year.
"We knew it wasn't going to be a quick turnaround," Peters said. "It takes time. ... I just like the direction we're headed in, and we're headed in that direction for a long period of time."
The Hurricanes used three rookies in the rotation on defense, and mounted a last-gasp -- but ultimately unsuccessful -- push for their first playoff appearance since 2009 by earning points in 12 of the 14 games that came after trading captain and franchise face Eric Staal to the New York Rangers.
Terms of Peters' extension were not disclosed. Peters was entering the final year of a three-year contract he signed in June 2014, when he was hired to take over for the fired Kirk Muller.
"You've got a head coach heading into the last year of his deal," Francis said. "It's important that if you like him and you want to have him around, you get this done."
The Hurricanes have reached the playoffs just once since winning the Stanley Cup in 2006. Carolina's seven-year postseason drought is the longest among Eastern Conference teams.
"Professionally, it's the right thing for me, and I want to see this thing through, and I want to get in the playoffs, and I want to get on a run," Peters said.