Sullivan signed a two-year deal worth up to $10.75 million in 2018. The decision to decline the option on the 33-year-old's contract will save the Rams $5.5 million in salary cap space, according to ESPN Stats & Information.
NFL Network first reported the news.
A source told ESPN that the Rams would discuss options with Sullivan for the 10-year veteran to remain with the organization in some capacity.
Brian Allen, a fourth-round pick from Michigan State in 2018, is expected to take over as starter.
Last season, the Rams were the only team in the NFL to start the same five players on the offensive line through 16 games, but turnover this offseason was expected.
Left guard Rodger Saffold, the Rams' longest-tenured player, will test the market as an unrestricted free agent.
Left tackle Andrew Whitworth, 37, mulled retirement, but recently announced that he would return for the final season of his three-year contract and 14th season as a pro. The right side of the line, featuring tackle Rob Havenstein and guard Austin Blythe, is expected to remain intact.
Second-year pro Joseph Noteboom, a third-round pick from TCU, could slide into the spot at left guard if Saffold signs elsewhere.
Allen and Noteboom received numerous practice reps last season because of Sullivan and Whitworth's weekly rest schedules, but both rookies played sparingly on offense as the Rams advanced to Super Bowl LIII.
The Rams initially signed Sullivan to a one-year deal in 2017 after he played the previous season for the Washington Redskins, where McVay served as offensive coordinator.
Sullivan's ability to diagnose a defense and communicate with quarterback Jared Goff proved invaluable.
In 2017, Sullivan started 15 games (McVay elected to rest starters in Week 17) as Goff rebounded from a difficult rookie season and helped the Rams to their first division title in 14 seasons.
Sullivan returned last season on his two-year deal and started every game as the Rams won a second consecutive division title and appeared in the Super Bowl for the first time since the 2001 season.
The Minnesota Vikings selected Sullivan in the sixth round (187th overall) of the 2008 draft. He played seven seasons with the Vikings and started 93 of 96 games, but was sidelined for the 2015 season because of back issues.