Wellwood had a career-high 47 points (18 goals, 29 assists) in 77 games with the Jets last season.
"For me to finally have a summer here where I'm able to prepare like you're supposed to for a hockey season and not have any injuries is great," Wellwood said. "I hope to get back where I was real early in my career."
He has played in 450 career games with Toronto, Vancouver, San Jose and Winnipeg, with 86 goals and 134 assists.
Wellwood was originally drafted by the Toronto Maple Leafs in the fifth round, 134th overall, of the 2001 draft.
Wellwood said he's excited to stay put in Winnipeg and start the upcoming season in a familiar environment.
"I'm excited about the signings they've had and way the team's going," he said. "It's going to be a good summer of getting prepared to improve."