GREEN BAY — At one point during his Tuesday evening news conference, Brian Gutekunst issued a subtle reminder that, technically, NFL free agency hadn’t even started yet.

“Nothing starts until tomorrow,” the Green Bay Packers first-year general manager said, referring to the league year officially kicking off at 3 p.m.

Gutekunst and the Packers are already off to quite the start, having agreed to terms with free agent tight end Jimmy Graham and defensive end Muhammad Wilkerson.

An NFL source confirmed that the Packers have deals in place with both Graham and Wilkerson. ESPN reported that Graham’s is a three-year deal, while NFL Network reported that Wilkerson received a one-year deal worth $5 million and an additional $3 million in incentives.

Entering free agency, Gutekunst had emphasized he wanted to be “aggressive” and “be in every conversation.” So on the same day as the team said goodbye to longtime wide receiver Jordy Nelson, who was released to create salary cap space, the Packers added a five-time Pro Bowl tight end in Graham to jazz up coach Mike McCarthy’s offense, and added Wilkerson, who visited the team after being cut by the New York Jets last week and could experience a rebirth under defensive coordinator Mike Pettine, who coached him in New York.

Amid some major spending across the league, the Packers seemingly picked their spots and added two veteran players they believe can help them.

“This is a big puzzle, and there’s limitations,” Gutekunst said of the big-money contracts being handed out and the decision to release Nelson after 10 years in Green Bay. “You try to stay as disciplined as you can, looking for the opportunity to improve your football team and being prepared to act if those opportunities present themselves.”

The 6-foot-7, 265-pound Graham, 31, spent the past three seasons with the Seattle Seahawks after breaking into the league with the New Orleans Saints as a third-round pick in 2010. Graham caught just 57 passes for 520 yards (9.1-yard average) last season with the Seahawks but did have 10 touchdown receptions.

The Saints, who traded Graham to the Seahawks in 2015 for center Max Unger and a first-round draft pick, were reportedly interested in bringing Graham back to New Orleans, where he caught at least 85 passes for four consecutive years and had monster seasons in 2011 (99 receptions, 1,310 yards, 11 TDs) and 2013 (86-1,215-16).

Whether Graham can regain that form in Green Bay remains to be seen, but tight end clearly was a need for the Packers.

Richard Rodgers, a 2014 third-round pick who has played more snaps at tight end for the Packers than anyone else the past four seasons, is an unrestricted free agent. The only other tight ends the Packers had on the roster before moving on Graham were ex-University of Wisconsin standout Lance Kendricks and youngster Emanuel Byrd.

This marks the third straight offseason in which the Packers have added an athletic veteran tight end in free agency, having signed Jared Cook in 2016 and Martellus Bennett last year. Cook was a gem of a signing but left as a free agent last March, while Bennett turned out to be a colossal mistake as teammates believe he quit on the team after quarterback Aaron Rodgers suffered a broken collarbone in October.

The 28-year-old Wilkerson, whom the Jets cut just two years into what had been a five-year, $86 million dealhe signed in the summer of 2016, entered the league as the 30th overall pick in the 2011 NFL draft and played his first two seasons under Pettine. He had two double-digit sack seasons before getting his new contract (10.5 in 2013 and 12 in 2015) but managed just eight total sacks over the past two seasons.

The Packers reached out to Wilkerson right away after his release became official last week, but Wilkerson took visits to three other teams before choosing the Packers.

Despite adding Wilkerson and Graham, the Packers still have work to do and Gutekunst admitted as much. Last week, Gutekunst traded 2015 first-round pick Damarious Randall to the Cleveland Browns for backup quarterback DeShone Kizer, leaving the team even thinner at cornerback than they were entering the offseason.

“I think we’ve got some good, young prospects (at cornerback),” Gutekunst said. “But that’s obviously a position we’re looking at heavily right now.”

Gutekunst also didn’t rule out releasing other veteran players to create cap room, although he did suggest that wide receiver Randall Cobb is safe, saying Cobb “is one of our good players, and we expect him to be.”

“We’ll look at every avenue to help improve our team,” Gutekunst said. “If it comes to difficult decisions, we’ll make them. But I think it’s important that we look at every avenue to improve our football team.”

Jason Wilde covers the Packers for ESPN Wisconsin. Listen to him with former Packers and Badgers offensive lineman Mark Tauscher weekdays from 9-11 on "Wilde & Tausch" on 100.5 FM ESPN Madison.