The Jets agreed to pay half of the $5 million that the contract called for a team to repay Denver for advance money already paid to the quarterback.
"This was an opportunity to add a dynamic playmaker," Jets general manager Mike Tannenbaum said.
"Mark (Sanchez) will be the starter and Tim will be the back up. This makes us a better football team."
Tebow, a Heisman Trophy winner with the University of Florida, helped lead the Broncos to the play-offs last season but was traded one day after Denver signed free agent Peyton Manning to a five-year $96 million deal.
The Jets had initially agreed to acquire Tebow by sending a fourth-round draft pick and a sixth-round selection to Denver, who sent a seventh-round pick back to the Jets along with Tebow.
"Tebow-mania just got a New Jersey address," the Jets had proclaimed on their website before discovering the payback provision that stalled finalization of the agreement.
With the deal in limbo, Tebow's hometown team the Jacksonville Jaguars re-entered talks and Tebow was given a choice of going to the Jets or the Jaguars and chose New York.
The deeply religious Tebow became one of the talking points of the NFL last season after he stepped in as starting quarterback and helped the Broncos overcome a 1-4 start with a six-game winning streak to finish the season 8-8 and win the AFC West title.
An 80-yard touchdown pass by Tebow on the first offensive play of overtime then lifted Denver to victory over the Pittsburgh Steelers in the first round of the play-offs.
They were knocked out a week later by the New England Patriots, who went on to reach the Super Bowl.
The Jets also finished last season with an 8-8 record, but fell out of play-off contention in the AFC East by losing their final three games.
The move by New York came after the Jets had signed their young starting quarterback Sanchez to a contract extension.
Tebow, a powerful runner and charismatic leader who completed only 46.5 percent of his passes last season, was expected to serve as back-up and to run a New York version of the Wildcat offensive package.
After last season, the Jets named Tony Sparano as offensive coordinator. Sparano was the architect of the Miami Dolphins' successful introduction to the NFL of the run-pass, old-time formation when he was head coach there.
Tebow, a former first-round draft pick, became a sports and cultural phenomenon last season.
A college-style quarterback whose public displays of his religious faith polarized public opinion, Tebow inspired a wide following of fans.
The phrase 'Tebow Time' was coined to capture the fact that five times his Broncos won games with late comebacks despite his woeful completion rate.