Simon had 27 points (10 goals, 17 assists) and 75 penalty minutes in 67 games last season. He can also earn more in the new deal in performance bonuses.
"Chris is just one of those old school guys who gave our team a little bit of everything last season," Islanders head coach Ted Nolan said in a statement. "We can't overstate Si's leadership.
"He'll have a big role with our team, just like last season."
Simon still has five games to serve next season on the 25-game suspension he received for a stick-swinging incident with New York Rangers forward Ryan Hollweg.
The 35-year-old Wawa, Ont., native was an unrestricted free agent but didn't come close to leaving.
"I take a lot of pride in being an Islander and I didn't consider playing anywhere else this season but on Long Island," Simon said in a statement. "Everyone knows the respect I have for Ted Nolan but it goes well beyond that.
"Everyone connected with the Islanders, from the owner to the fans, have been first-class. I cannot wait to get the season started."
Also on Monday, the Pittsburgh Penguins re-signed defenceman Alain Nasreddine, 32, to a one-year contract.
Laich, meanwhile, went to arbitration in Toronto, the first of six possible hearings this week. The 24-year-old Wawota, Sask., native had 18 points (8-10), a minus-2 rating and 29 penalty minutes in 73 games last season while earning $606,100. The forward has two NHL seasons under his belt.
The arbitrator's decision is expected within 48 hours.
Tuesday's scheduled hearing has a little more pizzazz to it, with Ottawa Senators starting goalie Ray Emery getting his turn to bat. His agent, J.P. Barry, and Senators GM Bryan Murray spoke over the weekend but got no closer to a deal.
"We have a gap in the way that we see the comparable goalies in this case," Barry told The Canadian Press on Monday. "And that's causing us a problem in coming to a resolution.
"It may just be necessary to arbitrate this case."
Both sides have comparables they fancy, the Senators can easily point to the $2.66-million salaries Buffalo's Ryan Miller and Carolina's Cam Ward earn as well as the $1.6 million Pittsburgh's Marc-Andre Fleury will make next season.
The Emery camp can counter with the two New York starters - Rick DiPietro and his $4.5-million salary on Long Island and the recent $4.25-million, one-year deal signed by Rangers star Henrik Lundqvist.
No arbitration hearings are scheduled for Wednesday after Joni Pitkanen settled with Edmonton last Friday. But Nick Schultz and the Minnesota Wild as well as Antti Miettinen and the Dallas Stars remain slated for hearings Thursday.
On Friday, Derek Roy and the Buffalo Sabres are on tap as well as Christoph Schubert and the Senators. Roy's agent, Larry Kelly, met with Sabres GM Darcy Regier over the weekend.
The hearings run through Aug. 3.