Tebow, who became one of the NFL's most popular players last season by helping Denver on an improbable run to the playoffs, was traded to the Jets after the Broncos signed free agent quarterback Peyton Manning last week.
"Me and Mark have had a great relationship for the last three years," Tebow told reporters at an introductory news conference.
"We text back and forth, we talked already. We're going to have great relationship and a great working relationship, and I think we'll have a lot of fun together."
Some local reports suggested the 25-year-old Sanchez, who led the Jets to the AFC title game in his first two seasons before struggling to an 8-8 mark last year, was confused over why New York were bringing in Tebow.
"From my conversations, he was excited," Tebow said. "Hopefully we'll be able to thrive together."
After making the trade, Jets general manager Mike Tannenbaum said Tebow, 24, would be used in special Wildcat packages where he could use his ability to run and pass.
"I've always said that I'm a football player first and then a quarterback, although that is my dream, that's what I want to be and what I believe I am," Tebow said.
"But however I can help a team, and make a difference, I'll be open to it and work as hard as I can."
Tebow said he was excited about joining the Jets and appreciated their on-field persona under head coach Rex Ryan.
"It's a physical team and a football team that has won a lot of games the last few years," said Tebow. "And hopefully by me being here we can be a little bit better and I can add something to this team and that is my hope and prayer.
"When you watch the New York Jets play you see a team that's physical, that wants to win and that's exciting. It's always a lot of fun to be on the tough team, the physical team."
Tebow said while use of Wildcat formations has dwindled since the Jets' new offensive coordinator Tony Sparano used it when he coached the Miami Dolphins, he believed it could be successful.
"When you have ability to have five, six people with an opportunity to touch the ball, I think that can be confusing and make defenses play slow," said Tebow, about the formation that creates confusion over who will take the snap.
"And I think when you have a great offensive coordinator like coach Sparano that can put together packages and plays and not have tendencies, then I think it can be effective."
Tebow would not say he coveted the starting quarterback job, but relished the opportunity to compete for a more expanded role.
"Everybody that puts on a uniform, you want to go out there and you want to play. That's why you play the game of football," he said.
"Whatever my role is, however I can expand that role I'm going to try to do that. And every day in practice I'm going to go out there and compete and get better as a quarterback and try to figure out any way possible to help this team any way I can."