Drafted 41st overall out of Georgia, Glenn is being given the opportunity to compete for the starting job at left tackle after Buffalo lost Demetress Bell in free agency this offseason.
Glenn is listed at 6-foot-6 and 345 pounds, and had 50 starts in 53 career games with the Bulldogs. He's one of three offensive linemen the Bills selected in last month's draft.
The move was announced Friday, and comes a day after the Bills signed their first-round pick, cornerback Stephon Gilmore.
Buffalo has now signed eight of its nine draft picks. That leaves receiver T.J. Graham, a third-round selection, as the only prospect unsigned.