Eaves has spent the last two seasons with Stars, but saw a 10-point decline in 2015-16.
The forward put up 11 goals and 17 points in 54 games, but played a much more valuable role during the playoffs, tallying three goals and six points in nine games.
Vanek had his worst statistical season in 2015-16, failing to hit the 20-goal mark for the first time since he joined the league during the 2005-06 season.
The 32-year-old managed just 18 goals and 41 points, and subsequently saw the final year of his contract bought out by the Minnesota Wild. Still, Vanek has two 40-goal campaigns to his name.
The club has signed forward Matt Martin to a reported four-year, $10-million contract, according to Bob McKenzie of TSN.
The 27-year-old winger scored a career-high 10 goals for the New York Islanders last season, albeit on an inflated 11.6 shooting percentage. He also added nine assists, tying a previous single-season high.
Martin, however, is not known for his scoring. He led the NHL in hits with 365 (4.6 per game) in 2015-16, and has been at the top of this category in each of the past five seasons.
The 24-year-old got his first taste of the NHL this season, suiting up in 23 games with the Canadiens.
Carr proved he could have value with the team going forward, posting six goals and nine points while being nearly a point-per-game player in the American Hockey League with 10 goals and 21 points in 24 games.
The Montreal Canadiens have agreed to terms with their top selection at this year's draft, signing No. 9 pick Mikhail Sergachev to a three-year entry-level contract.
The 18-year-old is coming off his first season with the Windsor Spitfires of the Ontario Hockey League, where he was named the league's defenseman of the year.
He tallied 17 goals and 57 points in 67 games during the regular season and added another five points in five playoff games.
Rundblad, the 17th overall pick from the 2009 NHL Draft, has appeared in 113 career games, recording four goals and 21 assists. He spent part of this past season on loan to Zurich SC of the Swiss League.
Paul Bissonnette could not sit idly while NHL free agents were raking in some serious cash.
General managers spent $544,829,124 total dollars in the first two hours of the signing period, leaving the former NHL forward to question his place in the hockey world.
— Paul Bissonnette (@BizNasty2point0) July 1, 2016
Bissonnette last appeared in an NHL regular-season game with the Arizona Coyotes in 2013-14. Time will tell if he does indeed fit into Toronto's "Shanaplan" or if he merely gets blocked on Twitter.
Wiercioch fell victim to a crowded Ottawa Senators back end, and wasn't extended a qualifying offer heading into free agency.
The 25-year-old only notched five points in 52 games with the Senators last season, but it could prove to be a low-risk, high-reward deal for the Avalanche, as he can slot in nearly anywhere.
The Tampa Bay Lightning have locked up another of their pending free agents, signing goaltender Andre Vasilevskiy to a three-year contract worth $10.5 million, the team announced.