The Patriots made Grissom a third-round choice in 2015. He played 37 games in four seasons in New England and made seven tackles, a sack and seven special teams stops.
He joined the Colts for the 2018 postseason and appeared on special teams in two games.
Grissom visited the Lions earlier this offseason before earning a spot with the Saints as a tryout player.
The Broncos made Williams a first-round draft pick in 2013. In six NFL seasons with Denver, Tennessee, Detroit and Miami, Williams has played 89 games with 63 starts.
Williams has 128 career tackles, 21 tackles for loss, six sacks, two passes defensed and a fumble recovery. In 2018, he played 14 games with four starts split between the Lions and Dolphins and finished with 14 tackles.
The Saints also announced the signings of fullback Michael Burton, receiver Cyril Grayson Jr., center Marcus Henry, tackle Ulrick John, linebacker Colton Jumper, running back A.J. Ouellette, defensive back David Simmons Jr. and receiver Micah Wright.
The team waived running back Darnell Holland, defensive lineman Tomasi Laulile and cornerback Darius Williams.