Primarily a left-back but also able to play at centre-back, the 20-year-old joined Everton from MK Dons in August 2014 and made his Premier League debut in May 2015.
He managed 14 starts last term under Roberto Martinez, whose replacement Ronald Koeman has allowed the Zimbabwe-born player to seek more regular first-team action at The Hawthorns.
According to West Brom's statement announcing the deal on Monday, Everton are not able to recall Galloway during the campaign.
"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," Galloway said.
"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."
In a slow transfer window for Tony Pulis' team, Galloway follows West Brom's only permanent signing, winger Matt Phillips, in moving to the Baggies.