Terms of the contract were not disclosed, but league sources told ESPN NFL Insider Adam Schefter that Tebow signed a two-year contract that includes no guaranteed money.
"Tim is a talented player, is smart and works hard. We'll see how it goes," Patriots coach Bill Belichick said Tuesday.
Tebow is wearing Jersey No. 5 at the team's mandatory minicamp, according to the roster distributed to the media by the Patriots. He has worn No. 15 in his first three NFL seasons but that number belongs to backup quarterback Ryan Mallett.
Tebow was signed to be a quarterback on the Patriots' roster, sources told ESPN NFL Insider Ed Werder.
When asked what position Tebow will play, Belichick said, "we will see."
Apparently tired of the Tebow questions, the coach tried to change the subject after several minutes.
"We've already talked enough about him. We'll see how it goes, take it from there," he said.
Former NFL quarterback Chris Weinke, who has been working with Tebow over the past month to tweak his throwing mechanics, told USA Today Sports that he believes Tebow can play quarterback in the NFL.
"Like I told Tim when I found out [Monday] that he signed, 'You're locked and loaded, ready to go,' " he told the newspaper.
The move reunites Tebow with Patriots offensive coordinator Josh McDaniels, who was the Broncos' head coach when Denver traded into the first round to draft the Heisman Trophy winner in 2010.
Belichick often has spoken with admiration of Tebow's versatility, intelligence and character. Belichick covets what he has described as tough, smart, versatile football players.
Last month, Yahoo! Sports cited an "organizational source" as saying Belichick disliked Tebow as a player and there was "no chance" of him landing in New England. Belichick dismissed that notion last week, telling ESPNBoston.com that the report was completely untrue.
Ironically, Tebow's last NFL start came in Denver's blowout playoff loss in Foxborough to Tom Brady and the Patriots following the 2011 season.
Tebow, 25, figures to compete with Mallett for a backup job behind Brady. The Patriots also released reserve quarterback Mike Kafka on Monday.
The Jets traded a pair of draft picks to Denver in the March 2012 deal to acquire Tebow but failed to establish a consistent role in the offense for the versatile quarterback, who attempted just eight passes, rushed for 102 yards on 32 carries and was used mostly to protect the punter.
"Unfortunately, things did not work out the way we all had hoped," Jets coach Rex Ryan said in a statement when Tebow was released.
Tebow helped the Broncos win the AFC West in 2011 and beat Pittsburgh in a wild-card playoff game before being traded to New York when Denver signed Peyton Manning.
Tebow's NFL career appeared over this offseason when the Jets couldn't trade him at draft time and wound up cutting the left-handed quarterback, who won the 2007 Heisman Trophy at Florida. There even was speculation he couldn't get an offer from any Canadian Football League teams.
Tebow has been criticized for his throwing motion but has said he wants to play quarterback, not switch positions. Still, the Patriots could need help at tight end after Rob Gronkowski underwent a fourth operation for a broken forearm and faces back surgery.
Belichick also has been willing to gamble on players discarded by other teams. Some have succeeded, such as wide receivers Wes Welker and Randy Moss and running back Danny Woodhead. Some haven't, including wide receiver Chad Johnson and defensive lineman Albert Haynesworth.
The media circus that surrounded Tebow at Florida, Denver and with the Jets could be minimized by Belichick, who keeps a tight lid on players' interactions with reporters.
Information from ESPN NFL Insiders Adam Schefter and Ed Werder, ESPNBoston.com's Field Yates and The Associated Press was used in this report.