FLORHAM PARK, N.J.—Tim Tebow finally will make his Jets debut Sunday against the Buffalo Bills. Once he does, he will end months of speculation about what exactly his role will be.

Yes, the Jets already have acknowledged that Tebow will run the “Wildcat” offense and serve as the up-back in punt formations. But their clandestine approach to his assimilation into the offense—they didn’t use the Wildcat in any of their preseason games, and they instituted a media blackout during practices—has lent an air of mystery to the Tebow...