The 20-year-old enjoyed a breakthrough campaign for the Toffees last season, making 14 Premier League starts thanks largely to an injury to Leighton Baines.
However, new boss Ronald Koeman has now sent the full-back to The Hawthorns for the 2016-17 campaign, where he will wear the number 20 shirt.
"I'm delighted. It's a great club and I'm really looking forward to getting started," he told the club's official website.
"My aims are to play and work hard for the team and help win as many matches as I can, it's all about winning.
"I think for me personally, it's really important to gain more experience. Coming here is the perfect opportunity to do that. I can't wait to get started and put the shirt on."
Galloway, who becomes West Brom's second signing of the summer, could make his league debut for the club at home to newly-promoted Middlesbrough this weekend. body check tags ::