Washington left Penn State with the 10th most receptions in program history.
Shorter appeared in 14 games for the Nittany Lions before transferring to Florida.
Clifford becomes the first Penn State quarterback to be selected in the NFL Draft since Trace McSorley.
"This is an unreal moment, and I'm just proud."
Brown is the fourth Penn Stater to hear his name called in this year's draft.
Scruggs is the first former Penn State center to hear his name called in the draft since Michal Menet in 2021.