Tebow, 25, is being reunited with Josh McDaniels, the Patriots offensive coordinator who was Denver's head coach when the Broncos traded into the first round to take him with the 25th draft pick in 2010.
There is no guarantee that Tebow will still be with the Patriots when training camp begins next month, but if the Patriots keep him, he would have time to develop as a quarterback since Tom Brady holds that job. Tebow even could be tried at tight end, where the status of Rob Gronkowski is uncertain after he had his fourth operation on his broken left forearm on May 20 and faces back surgery this month.
Tebow's NFL career appeared to be over when the Jets released him on April 29 and no team rushed to sign him. But Patriots coach Bill Belichick decided to bring in the 2007 Heisman Trophy winner who led Florida to two national championships.
After the NFL draft, in which they selected quarterback Geno Smith from West Virginia, the Jets decided to release Tebow just more than a year after a dressed-up, high-profile press conference that welcomed him to the organization.
New York went 6-10 last season, lost its final three games and finished tied for last place in the AFC East with Buffalo. New England, meanwhile, went 12-4, won the division and advanced to the AFC title game.
"I felt like it was a learning opportunity for me. There was a lot that I'll take from it," Tebow said at the end of the season. "There's a lot that I learned, and there are lot of relationships that I've built, so I know that it happened for a reason."
Now, he joins a rival who swept the Jets last season, including an embarrassing 49-19 loss that New York endured at home on Thanksgiving night.
"We have a great deal of respect for Tim Tebow. Unfortunately, things did not work out the way we all had hoped," Jets coach Rex Ryan said in April. "Tim is an extremely hard worker, evident by the shape he came back in this offseason. We wish him the best moving forward."
The last time Tebow threw a pass in Foxborough, Denver lost in the divisional playoff round to the Patriots 45-10 in the 2011 season. He completed 9 of 26 passes for 136 yards with no touchdowns or interceptions and five sacks in that game and gained 13 yards on five rushes.
When he was traded to the Jets with great fanfare in March 2012, there was speculation he might replace Mark Sanchez as the starting quarterback. But when Sanchez struggled, he was replaced by Greg McElroy late in the season. Tebow threw only eight passes all year and played primarily as the protector for the Jets' punter.
Tebow's presence on the team and absence from the field fed a media frenzy in New York.
The spotlight will be dimmer in Foxborough where Belichick tightly controls which players can talk to the media and what they can say. When they go beyond those limits, Belichick sometimes forbids them from talking with reporters.
Former Broncos general manager Ted Sundquist sees the logic in the Patriots' decision to bring Tebow to minicamp.
"If you can find a club that's mature enough to handle it as an organization, then you're going to find the right spot for him," Sundquist said. "What I mean by that is all the media mania and that sort of thing. The club says, 'Look, this is the reason we're bringing him on. We feel he can bring X, Y, Z and A, B, C to the table.'
"Explain it to Tim, explain it to the media, explain it to your fan base and explain it to your organization."
The Patriots run a complex offense and Tebow had trouble grasping the strategy in Denver. But the presence of McDaniels could help him.
"If there's one guy in the NFL who's a fan of Tim Tebow or pulling for him, it would be Josh McDaniels," said former Jets and Patriots offensive lineman Damien Woody, now an ESPN analyst.
"I think they'll take their time developing him," Woody said. "The Patriots are one of those teams that like to develop guys, and they'll even trade them if it works in their favor. In the more immediate future, having played in New England, I know one thing they value is versatility. They're going to try to use Tebow in positions where they feel they can maximize his talent."
As an NFL rookie in 2010, Tebow threw just 82 passes in nine games, starting three.
In 2011, he started 11 games and threw for 12 touchdowns and six interceptions. He led Denver to a wild-card win over Pittsburgh before the divisional loss to New England.
He was traded to New York after that season when Denver signed Peyton Manning. With the Jets, Tebow completed six of eight passes and ran 32 times for 102 yards.
In addition to Brady, the Patriots also have Ryan Mallett at quarterback already, but they released Mike Kafka on Monday.
The 2007 winner of the Heisman as a sophomore at Florida, Tebow has 2,422 passing yards and a 75.3 rating as an NFL quarterback.