Galloway first of a two expected signings to arrive from Merseyside
Galloway is the first of two expected loanees to arrive on Wearside from Everton, with fellow defender Tyias Browning also rumoured to be close to joining the Championship club.
The Zimbabwean-born man has turned out for England at U17, U18, U19 and U21 level and spent last season on loan at West Bromwich Albion for whom he made five appearances.
The 21-year-old, who can play either as a left-back or centre-back, began his career at MK Dons and came through their youth system before making the move to Merseyside in 2014.
Galloway has gone on to make 20 appearances for the Toffees since then, including his Premier League debut away to West Ham United in the 2014/15 campaign.
Internationally, he turned down the opportunity to play for Zimbabwe in the 2017 Africa Cup of Nations in favour of staying with the England U21's with the aim of working his way up towards the senior team.
Captain's new deal provides stability on Wearside
In terms of other signings the Wearsiders have recently been linked with a move for another Everton player in Aiden McGeady, who impressed while playing under Grayson on loan at Preston North End last season.
Jermain Defoe, Jordan Pickford and Fabio Borini have all left the club in permanent transfers to AFC Bournemouth, Everton and AC Milan respectively while club captain John O'Shea has committed his short-term future to the club by signing a one-year contract extension.
O'Shea, who is now the club's leading appearance maker in the Premier League with 182 top-flight appearances, told the club's official website that he was "delighted" to sign a new deal on Wearside and acknowledged that the club have a "big job on [their] hands" this season.