FOXBOROUGH, Mass. -- Tom Brady became the NFL’s all-time winningest quarterback on Sunday, while the former New England Patriots teammate he leapfrogged for the starting job in 2001 reflected on his doubts that Brady would ever win one game, let alone 201.

“I don’t think anybody really saw the run that he’s been on coming,” former Patriots quarterback Drew Bledsoe said. “I figured he’d be around the league for a long time, because he was a hard-working guy that had a great attitude. But I don’t even know that I ever thought he would be a starter; he was just this skinny kid out of Michigan.”

That kid, now 39, has his name atop the NFL record book over some of football’s all-time greats, passing Peyton Manning (200), Brett Favre (199) and John Elway (162). Brady secured the record when the Patriots defeated the Los Angeles Rams 26-10 on Sunday.

In an email to ESPN.com, Elway paid respect to Brady, saying, “One thing about Tom Brady is that he's obviously had a tremendous career, but he is a team guy. He's been a team guy from the start. If you're going to ever ask Tom what's the most important record that he will hold, my guess is he would say that having the most wins of any quarterback in the history of the league is going to be the most important. That's the mentality that he plays with and why he's been so successful."

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Elway and Brady will have a chance for another face-to-face meeting later this month when the Patriots visit the Denver Broncos on Dec. 18.

Brady seems to embrace those conversations, such as the one he had with Pro Football Hall of Famer Jim Kelly on Oct. 30 after the Patriots-Bills game in Orchard Park, New York. The next day, Kelly shared with ESPN his belief that Brady is the best quarterback of all time.

“I don’t mind saying that,” Kelly told ESPN’s Chris Berman. “The consistency, every single year he does it. And he doesn’t have, all time, the greatest players around him ... but the thing is he makes it work, and it doesn’t matter what it is.”

Brady and Kelly have exchanged text messages for years, and Brady said he values their friendship. It’s a similar situation with current New Orleans Saints quarterback Drew Brees, who praised Brady on the cusp of his victory No. 201.

“It’s probably the most important stat. There’s no surprise. He’s earned it,” said Brees, who last connected with Brady during joint practices in early August.

“He will go down certainly as one of the best, if not the best, for that reason. The guy is a winner; he’s a proven winner. While he’s been there with Coach Belichick and had that level of consistency, there’s been a lot of players come through there when he’s been there, and it’s been a very consistent result all the time. I’m sure there are many in that building that deserve credit, but none more so than him.”

That sustained success also has impressed Favre.

“I think the more he plays, the more competitive he gets,” Favre said on his weekly Sirius XM NFL Radio show. “He is just determined time in, time out, to prove everyone wrong. And not that I doubt him or anyone else doubts him, but he kind of uses that as an edge. He doesn’t need an edge; the guy is so good.

“He’s just a winner, a gamer, and I love to watch his competitiveness. I would never bet against him, that’s for sure.”

Favre added, “As far as records go, he can break as many as he wants, because I think he’ll play as long as he wants and be good up until the day he leaves. He’s that impressive.”

On Saturday night, Brady joined Bledsoe and 40 other teammates at Gillette Stadium as part of a celebration of the 15-year anniversary of the Patriots’ Super Bowl XXXVI championship team.

That was the season Brady picked up the first of his 201 wins.

“The fact that Tommy is still playing at the level he’s at is pretty impressive,” Bledsoe said. “He’ll wear everyone out talking about his diet and workout regimen, but it’s working. That, combined with that you can’t hit the quarterback these days, is going to allow him to play a lot longer.

“He takes great care of himself, and he’s been such a great leader for this organization.”