Both players have been medically cleared and are expected to be ready to practice on Thursday morning when the Packers open camp.
Nelson had offseason hip surgery and Hayward was dealing with a foot injury. Oft-injured linebacker Nick Perry, who missed time with a shoulder injury, was also cleared on Wednesday.
The news wasn’t as good for another veteran outside linebacker.
Mike Neal, who has some kind of phantom injury, flunked his physical and was put on the physically unable to perform list. He was joined there by undrafted rookie running back John Crockett and receiver Ricky Collins.