The Bills announced the signings and Anderson informed the NFL of his retirement on Thursday, a day before opening their rookie minicamp.
Anderson's decision to retire comes as a surprise, after the 35-year-old signed a one-year contract a day after Buffalo closed its season. The Bills lured him out of semi-retirement in October to serve as an experienced backup to then-rookie Josh Allen.
Anderson started two games in place of an injured Allen before being sidelined with a concussion. This season, he was projected to be Buffalo's third-string quarterback, behind Matt Barkley, and serve as Allen's mentor.
The Bills added a quarterback Thursday by signing Tyree Jackson, an undrafted free agent out of the University at Buffalo.
Oliver is a defensive tackle out of Houston, and drafted ninth overall two weeks ago.
Buffalo also signed second-round pick, offensive tackle Cody Ford, as well as running back Devin Singletary, the first of the team's two third-round picks. Also signing their rookie contracts were linebacker Vosean Joseph, safety JaQuan Johnson, defensive end Darryl Johnson and tight end Tommy Sweeney, who were selected in the final three rounds.
The Bills' lone unsigned draft pick is tight end Dawson Knox. Buffalo traded both of its fourth-round picks to move up in the draft order to choose Knox in the third round.
The Bills also announced signing seven other undrafted rookies, including Buffalo cornerback Cam Lewis.
Also signed were linebackers Tyrel Dodson (Texas A&M) and Juwan Foggie (Charlotte), receivers David Sills (West Virginia) and Nick Easley (Iowa), Northwestern offensive lineman Blake Hance and Illinois kicker Chase McLaughlin.