Galloway, 21, has made 21 appearances for the Toffees since joining from MK Dons and also played five games for West Bromwich Albion on loan last term.
The Zimbabwe-born England Under-19 international can play centre-half or left-back.
He is new manager Simon Grayson's first signing for the Black Cats, following his move from Preston this summer.
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Everton have loaned defender Brendan Galloway to Championship newcomers Sunderland on a season-long deal.