With two new players joining the team this week, the Twins took care of the existing roster on Monday.

The entire roster of unsigned players was offered 2014 contracts before Monday night’s deadline, a formality for all but three. Relief pitchers Brian Duensing and Anthony Swarzak as well as third baseman Trevor Plouffe are eligible for the salary arbitration process, but all were too valuable in 2013 for the Twins to let them walk away.

Had the Twins chosen not to tender contracts to that arbitration-eligible trio by Monday’s 11 p.m. deadline, they could have become free agents. Instead, the three will negotiate raises on their salaries for next season or file to have an independent arbitrator decide how much they’ll earn, a process the Twins have avoided for nearly a decade.

Duensing, who earned $1.3 million in 2013, his fourth season with the Twins, and Swarzak, who made $502,500 in his third year, are eligible for arbitration because they have more than three seasons of service time. Plouffe, paid $520,000 last season, is among the top 22 percent of two-year players in terms of service time, making him eligible as a so-called “super-two” player.

It’s likely that Duensing, who posted a 3.98 ERA in 61 innings, and Plouffe, who batted .254 with 14 home runs, will earn $2 million or more when their contracts are settled, while Swarzak can expect to roughly double his salary. Salaries are normally agreed to without a hearing; no major league player had his case heard by an arbitrator last winter. The Twins have not been taken to a hearing by a player since Kyle Lohse, who won his case against the Twins in both 2005 and 2006.

The Twins’ roster stands at 39, but that will increase to 40 on Tuesday, when righthanded pitcher Ricky Nolasco signs the largest free-agent contract in franchise history — a four-year, $49 million agreement that more than doubles the $21 million contract of Josh Willingham, the previous record-holder. The team has called a 2 p.m. news conference Tuesday at Target Field to introduce Nolasco.

Minnesota also has an agreement with former Yankees righthander Phil Hughes on a three-year, $24 million contract, which — once it’s signed — will require another roster move to make room.

The addition of those two free-agent pitchers likely clears the way for General Manager Terry Ryan to address the team’s meager offense next week at baseball’s Winter Meetings in Orlando, Fla. He’ll do so with only about $77 million committed to major league salaries next year, depending upon what Swarzak, Duensing and Plouffe eventually get. That leaves Ryan with plenty of room to maneuver; last year’s payroll was $82 million, while the previous two seasons eclipsed $100 million.