The 19-year-old full-back was handed his chance at first-team level at the end of last season following injuries to Leighton Baines and Bryan Oviedo and has not looked back.
Galloway, who has made 16 appearances this season, told the club's official website: "I'm really happy to commit my future here.
"This is a club that has got so much young talent and is moving forward
It's great to be able to commit to being a part of that.
"My family came up to watch me sign so it was nice to have them around
They have been with me all the way."
The Zimbabwe-born player began his career with MK Dons before joining Everton in August 2014 on a five-year deal.
Toffees boss Roberto Martinez said: "Brendan arrived at the football club with a very clear development path in front of him but the reality is that he has surpassed that
"Then he joined the first team environment and he has developed into an important player and a very good performer
At Everton we will always reward those who deserve it.
"This is another step forward
He is still a young man but one with a fantastic personality
This is a day for him to celebrate with his family, but also one for everyone connected with Everton to recognise a young man who has come through and done so well."
Galloway, who has also been called up by England Under-21s this season, is likely to start again against Norwich on Saturday but faces a battle to hold onto his place with Baines now fit again.
Source : PA
Source: PA