Browning will be reunited with Sunderland coach Simon Grayson, after he spent the second half of the season on loan at Preston.
The U-21 international has played nine games for Everton since his debut in September 2014. He has also played for England U-17, U-19 and Under 21 levels.
On Wednesday, Sunderland signed the defender on a season-long loan deal. Sunderland also want to sign Bournemouth's forward Max Gradel on a season-long loan deal.