The midfielder will have his medical scheduled at West Brom ahead of finalising a move to the Hawthorns.
The Brentford midfielder joined the club in 2016 and has become a key player for the side. However, the Bees have decided to cash in on him as he has only a year left in his contract.
The news will come as a blow for Leeds United who showed interest in signing the 27-year-old.
Earlier this month, the Daily Record reported that the Yorkshire club have joined the race for him alongside Scottish Champions Celtic.
However, West Brom have moved quickly to secure his services, and the midfielder is likely to become their next signing.
Brentford have signed Celta Vigo’s Mathias Jensen for £3.5m this summer as a replacement for Sawyers.