Chillar's agent, Jim Ivler, said Wednesday the contract contains incentives that could raise its overall value to $6.4 million.
"I won't say that they committed to a role, but based upon my confidence in my client, I believe he'll compete for the starting job," Ivler said.
Chillar is the first free-agent signing this offseason by the Packers, who have taken a restrained approach to spending money on the market under general manager Ted Thompson.
The team has given contract extensions to several of its own marquee players but signed only one free agent last offseason, giving a one-year deal to backup cornerback Frank Walker. Walker signed with the Baltimore Ravens last week.
Green Bay also is in the market for a veteran backup quarterback after Brett Favre retired earlier this month, leaving the starting job to 2005 first-round pick Aaron Rodgers. The team reportedly has shown interest in Gus Frerotte and Quinn Gray.
The 6-foot-3, 242-pound Chillar started 15 games for the Rams last season, making 65 tackles, including 52 solos. He had a career-high 2½ sacks and three forced fumbles.
Chillar, 25, was a fourth-round pick out of UCLA in the 2004 draft by St. Louis.
The Rams reportedly were interested in keeping him, and he also drew interest from the Arizona Cardinals.