Brown was set to make $2.7 million and account for $3.7 million against the cap next season, the final year of his five-year, $14.2 million deal.
Brown, 32, is a nine-year NFL veteran who joined the Rams in 2008 after spending five seasons with the Seattle Seahawks. He has made 220 of 272 field-goal attempts in his career, but he was just 21 of 28 last season.
Zuerlein, the 171st overall pick, set an NCAA Division II record with 21 consecutive field goals last season and missed only once in 24 tries overall.
Follow Jason La Canfora on Twitter @JasonLaCanfora.
The Associated Press contributed to this report.