No financial terms were reported for either player. The contracts cannot be finalized until the new league year opens on Wednesday at 4 p.m. ET.
Nelson spent the previous four seasons with the Denver Broncos. He appeared in all 16 games over his first three seasons with Denver, making six starts and setting a career high with 61 tackles and five passes defensed in 2016.
However, a torn biceps sustained in practice ended Nelson's season after five games in 2017. A former seventh-round draft pick out of Oklahoma, Nelson also saw time on special teams with the Broncos.
Ngata, 34, had similar injury problems while with the Detroit Lions in 2017. He started the first five games of the season, but suffered a torn biceps in Week 5 and finished the season on injured reserve.
Ngata is a five-time Pro Bowl selection (2009-2013) who has started 165 of the 167 NFL games in which he has played.
Eagles defensive tackle Beau Allen is scheduled to be a free agent this offseason, so Ngata serves as a replacement for him.