The Bills will move up to the No. 12 pick in the draft and also acquired the 187th overall selection from the Bengals, who will now pick 21st in the first round and have the 158th overall pick.
The 28-year-old Glenn is signed through 2020.
He is set to make $11.25 million this season with the salary cap hit set to shrink the next two seasons according to spotrac.com.
Adding that salary for this season, though, has reportedly forced the Bengals to pare down their list of potential signings as they are also putting aside money to extend the contracts of some veterans.