Shields, 30, didn't play last season after the Packers released him in February. Before he was released, he had played in just one game in 2016 and missed four games in 2015 because of concussions.
The former Pro Bowl cornerback never returned from the concussion he suffered in the Packers' 2016 season opener at Jacksonville. It was the fourth concussion of his NFL career and second in nine months.
"Some days it's tough headaches. Some days it's mild," Shields said in January 2017. "It varies. I never know. I'm so used to it that it's just normal. Like I said, each day it's getting better. I'll be back."
When healthy, Shields was one of the top cover cornerbacks in the league. He has 23 interceptions (including the playoffs) since entering the league in 2010. From 2012 to 2016, Peters generated either an interception or a pass defended on 16.2 percent of targets thrown into his coverage, fifth-best among corners during that stretch, according to Pro Football Focus.
Shields, who won a Super Bowl with the 2010 Packers and made the Pro Bowl in 2014, will provide the Rams with some much-needed depth at outside corner.
The Rams recently acquired All-Pro cornerback Marcus Peters in a trade with the Kansas City Chiefs. But their No. 2 corner, Kayvon Webster, is recovering from a ruptured Achilles tendon he suffered in December, and there isn't much depth behind him.
The Shields signing is yet another indication that the Rams don't have much confidence in their ability to retain Trumaine Johnson, who spent the past two seasons playing under the franchise tag and is expected to have a robust market in free agency.
Information from ESPN's Rob Demovsky and Alden Gonzalez was used in this report.