Schottenheimer parted ways with New York two weeks ago following a season in which the offense ranked 25th in the NFL and failed to break the 20-point mark in each of the last three games.
Schottenheimer had been the offensive coordinator of the Jets since 2006.
"I am really excited to have Brian join our staff," Rams head coach Jeff Fisher said. "He is a well respected coach in this league who has had success for many years at a high level as an offensive coordinator. We share the same philosophies on the offensive side of the ball and I think he is a tremendous addition to our staff."
Williams was the defensive coordinator for the Saints for the past three seasons. In his first year in New Orleans, Williams helped guide the Saints to a Super Bowl title.
Fisher and Williams are close friends, working together in Tennessee for six seasons. During his time in Tennessee, Williams helped lead the Titans to Super Bowl XXXIV.
In 15 seasons as a defensive coordinator or head coach, Williams has led seven top 10 defenses.
"I have worked with and known Gregg for a lot of years and I have a tremendous amount of respect for him as a defensive coordinator and value his past experience as a head coach," Fisher said. "He brings an aggressive approach that I'm sure will benefit our defense and he has a wealth of knowledge that will aid our entire team."
Williams was the head coach of the Buffalo Bills for three seasons after spending 11 years in Tennessee (1990-2000). He has also spent time in Washington (2004-07) as an assistant head coach/defense coordinator and a year as defensive coordinator in Jacksonville (2008).