Buffalo had until Monday to decide whether to match the Rams' offer sheet, which Groy signed Tuesday. The deal includes $3.5 million in guaranteed money and will include cap numbers of $2.5 million each season.
Buffalo gave Groy an original-round restricted free-agent tender earlier this month, worth $1.8 million. Because Groy was undrafted, the Bills would not have received any draft compensation if they declined to match the Rams' offer.
Initially a backup guard for Buffalo, Groy would have rejoined former Bills offensive line coach Aaron Kromer in Los Angeles and would have been expected to start at center for the Rams after Tim Barnes was released.