The deal is worth $6.75 million, according to multiple reports.
Zuerlein, 29, converted 19 of 22 field-goal attempts last season in a solid rebound from a shaky 2015. Zuerlein's job was in jeopardy when he was just 20 of 30 in the franchise's final season in St. Louis.
The five-year veteran has made 18 field goals of 50 yards or more in his career.
The Rams also signed center Ryan Groy, a restricted free agent, to a two-year tender worth $5 million. The Buffalo Bills have five days to match the offer.
Groy spent the past two years with Buffalo and started seven games last season. He also played for the Chicago Bears in 2014.