The 28-year-old becomes the fourth signing of the summer, after Alex Mowatt, Quevin Castro and Matt Clarke.
Reach totalled 231 for Sheffield Wednesday, the club he departed at the end of last season, following their relegation from the Championship.
The winger was delighted to secure his move to The Hawthorns, labelling it as the 'most exciting challenge' of his career.
"It’s clear that West Bromwich Albion is a very ambitious club." he said.
"I share those ambitions of wanting to play in the Premier League.
"It’s the most exciting challenge of my career and it’s certainly the biggest challenge of my career.
"I pride myself on making a lot of appearances for clubs. I want to make plenty of appearances here and have my best years here. I just's cant wait to get started."
Reach could feature in Albion's first game of the Championship season on Friday, when Valerien Ismael's side travel to Bournemouth.