Quinn finished second in the NFL with 19 sacks last season and has emerged as one of the league's top pass rushers since being drafted in the first round in 2011.
The 24-year-old Quinn, a Pro Bowler last season, has two years remaining on his existing contract with the Rams, meaning the extension will start in 2016.
Quinn headlines a talented St. Louis defensive line that also features Michael Brockers, rookie Aaron Donald and defensive end Chris Long, who is on short-term injured reserve with an ankle injury.
ESPN NFL Insider Adam Schefter and ESPN.com Rams reporter Nick Wagoner contributed to this report.
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