Stempniak, who split last season between the New Jersey Devils and Boston Bruins, had 51 points in 82 games, one point shy of his NHL career high with the St. Louis Blues in 2006-07.
"He's going to come in here and score and give us veteran leadership," Peters said. "You look at the [other] guys we've added, and they can skate. Stalberg has world-class speed. Bickell has above-average NHL speed. Teravainen is a gifted skater. I just like the direction we're headed in, and we're headed in that direction for a long time."
Peters coached Canada to a gold medal at the 2016 IIHF World Championship and will be an assistant for Team Canada at the World Cup of Hockey 2016.
"In the two years he's been here, he's done a tremendous job coaching," Francis said. "I think that's getting noticed in other places as well, with the opportunities with Canada. He's got an unending thirst for knowledge. He doesn't take a day off. If anything, it's me trying to pull him back here and there."
Peters said the job security won't make him complacent. He said he's learning how to best get his plans across to one of the youngest teams in the NHL.
"The team is getting younger and I'm getting older," he said. "As you get older you become a little more patient. That's something I can get better at for sure. The art of communication is important with the millennials too."