New England sprung first, snagging Auburn quarterback Jarrett Stidham with the No. 133 overall pick of the draft in the fourth round.
Philadelphia selected Northwestern gunslinger Clayton Thorson in the fifth round at No. 167 overall.
Thorson capped off his career as Northwestern's all-time leader in wins. He passed for 10,731 yards, 61 scores and 45 interceptions in his four seasons with the Wildcats. The 6-foot-4, 222-pound quarterback also scored 27 touchdowns on the ground.
The Eagles were in need of depth at the position after Nick Foles landed with the Jacksonville Jaguars this season. Nate Sudfeld joins Thorson behind Wentz in the Eagles' quarterbacks room. The Eagles also head into the off-season training program with Luis Perez, who will likely battle Thorson for the third-string job.
Brady's current backup is Brian Hoyer, but Stidham could push the veteran quarterback in camp for the No. 2 gig. Stidham completed 60.7 percent of his throws for 2,794 yards, 18 scores and five interceptions in 13 games last season at Auburn. The 6-foot-3, 215-pound gunslinger completed 66.5 percent of his throws for 3,158 yards, 18 scores and six interceptions in his sophomore season for the Tigers.