The 20 year-old defender will make the switch The Hawthorns with a view to a permanent move.
Galloway has a contract with The Toffees until June 2020.
Full-back makes West Midlands switch
Zimbabwe-born Galloway, made his first strides into football when he joined MK Dons U11 youth side and was hastily fast-tracked in the senior side.
Having made just 10 appearances for the League One side, the defender was snapped up by Roberto Martinez' side as an 18 year-old.
Galloway has played for England's international set-up from the U17 through to the U19s, having made 15 appearances but is yet to score for his adopted country.
Galloway broke through after Baines' injury
After Everton's regular left-back Leighton Baines sustained an injury in training, ruling him out for over three months - with Luke Garbutt having made the loan move to Fulham, Galloway was given his chance on the opening day of last season against Watford.
The youngster impressed and became a regular fixture in the absence of Baines, recording four clean sheet and assisting once.
For The Baggies, Galloway may slot straight in on Sunday as they entertain Middlesbrough, with Chris Brunt continuing his recovery from an ACL injury and Jonny Evans filling a makeshift role for Tony Pulis' men.
'Perfect opportunity' for defender
Speaking of his his arrival as West Brom, Galloway stated, “I’m delighted. It’s a great club and I’m really looking forward to getting started."
The 20 year old explains that, “my aims are to play and work hard for the team" and to "help win as many matches as I can".
“I think for me personally, it’s really important to gain more experience", says Galloway. In closing he adds, "Coming here is the perfect opportunity to do that. I can’t wait to get started and put the shirt on.”