Groy's deal reportedly includes $3.5 million in guaranteed money.
The Rams had aimed to make the 26-year-old Groy the second lineman to sign with them, joining veteran left tackle
Groy had signed the Rams' offer sheet Tuesday. The Bills had five days to match the offer or let Groy leave without compensation.
So the Rams remain in search of a replacement for the released Tim Barnes.
Groy appeared to be a good fit for a Rams team that must upgrade a line that last season failed to spring running back Todd Gurley or protect quarterback Jared Goff.
The Rams have added four free agents: Whitworth, receiver
The Rams were meeting Thursday with linebacker Connor Barwin.