Kevin Faulk and Stephen Neal had their chances on the free agent market this offseason, but when it came right down to it, there was no place they’d rather be than Foxboro.

The two veteran free agents, each of whom has played his entire career with the Patriots, officially signed contracts to rejoin the franchise this week. With both of them 33 years of age, they now could be poised to finish their pro careers in the same place they started. In an era of free agency, it’s a unique trait that both of them appreciate. On a conference call Thursday, two of the five players on the New England who were part of all three Super Bowl-winning teams talked about how the opportunity to go wire-to-wire with one team clearly means something.

“That is very rare. That’s one of the reasons I am still here,” said Faulk, who acknowledged he was “85 percent sure” he’d return to the Patriots, but still received offers from other teams.

“You see a lot of guys that come and go in the NFL, that have been with one team for a certain amount of years and they’ve left and go make their mark somewhere else,” he added. “But you never hear about a guy in this day and age that’s been staying for a long time. And it’s just a fact of being in that organization and trying to uphold and be consistent.”

“To be honest, I really didn’t want to leave, but I didn’t know if the Patriots really wanted me back,” Neal said. “One of the factors was I wanted to make sure I was wanted or needed somewhere. If something would have came up maybe I would have looked into it.

“In today’s game, it’s hard for people to sign with one team and be with them their entire career, and I think that’s something special and I’d like to do that.”

When it came to retirement, Faulk said he never really considered it, even chuckling at the thought on Thursday. But Neal’s decision was much harder: After New England’s playoff loss to Baltimore, he spoke openly about the possibility of retirement, and said on Thursday it took him until “two or three weeks ago” before he was comfortable with the idea of coming back to the game again.

“The entire time the playoffs were going on I didn’t know what I was going to do, Neal confessed. “I started doing some things and just being active because out here there are a lot of things to do outside – going for hikes with the family and doing some stuff and my body started to feel a little bit better and a little bit better and a little bit better.

“And then I called my agent, I told him if there is interest in someone signing me for football I think I’d like to go forward. So, probably just a couple weeks ago I decided I think I can get after it a little bit longer.”

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Faulk was taken in the second round of the 1999 draft, and is the only player remaining on the roster who was playing for New England before Bill Belichick took over as head coach in 2000. Over the course of his career, he has become an uber-dependable part of the New England offense — this past season, he was the only player to finish with more than 300 yards on the ground and in the air (Faulk ran for 335 yards and caught 37 passes for 301 yards and scored three touchdowns last season). For his career, he has 3,505 yards rushing and 418 receptions for 3,605 yards, and has also returned kicks and punts.

When it comes to building a legacy, Faulk brought up the case of Nomar Garciaparra’s retirement Wednesday. Faulk said it was nice to see Garciaparra’s ceremonial signing of a one-day contract that saw him leave the game as a member of his original team, the Red Sox. But in the end, it left him wondering what might have been.

“I might have left and gone and it might have been successful,” he said. “But it wouldn’t have been the same if I would have been here doing it.”

As for Neal, he never player college football, but signed with the Patriots as a free agent in 2001 and moved into the starting lineup for good in 2004. This past season, the right guard was part of a line that allowed 18 sacks last season, the team’s fewest since the league switched to a 16-game schedule in 1978.

By the sound of things, the only team that might have been able to lure Neal away from the Patriots was the Chargers, because Neal has family in Southern California. But if San Diego was ever interested in Neal, he never knew it.

“Driving to my parent’s house, I always drive by the Chargers facility, so it would be a fit,” he said. “I could be with all of my family, which is very important to me. My grandparents are getting a lot older and my parents are getting older, so it would be great to be able to spend the time with the family, and being in New England you can’t just go to San Diego for the weekend.

“With three kids, the time change on them and me and my wife Jodi, it’s pretty tough. That’s why I would consider playing for a team closer to my final destination of home. But, like I said, I really wanted to start my career somewhere and end it somewhere, and I think with this deal I don’t think I can play too much longer after two years.”