The deal will include $75,000 guaranteed, a source told ESPN's Adam Schefter.
Bills general manager Brandon Beane said Saturday he was surprised the 6-foot-7 Jackson was not among 11 signal-callers selected in the draft. Jackson was ESPN's eighth-ranked quarterback prospect and fourth-highest-ranked player not to be picked.
"I truly thought he would be drafted. He was on our draft board to be drafted," Beane said. "You start sitting there in the seventh [round] and thinking, man, if this guy doesn't get drafted we'll have to go after him."
The Bills were not expected to be in the quarterback market this offseason after drafting Josh Allen with the No. 7 overall pick last year and extending the contracts of veteran backups Matt Barkley and Derek Anderson late last season.
Jackson, 21, becomes the sixth quarterback in NFL history listed at 6-foot-7 or taller, according to ESPN Stats & Information research. Only Paxton Lynch remains in the league.
In 14 games for Buffalo last season, Jackson completed 55 percent of his passes for 3,131 yards, 28 touchdowns and 12 interceptions. With one season of eligibility remaining, Jackson decided to declare for the draft despite the NFL's college advisory committee not assigning him a first- or second-round grade and suggesting he remain in school.