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Pickford was Everton manager Ronald Koeman's top target to take over from Maarten Stekelenburg and Joel Robles, who both endured inconsistent spells last season.
Sunderland have accepted an offer from Everton which could rise to £30 million with various add-ons included in the package.
England Under-21 international Pickford was one of the few bright spots as Sunderland were relegated from the Premier League last season.
He earned a call-up to England's senior ranks in October and has represented the country at each of the six youth levels from Under-16 upwards.
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Should the terms of each of the add-ons be met, Pickford would become Everton's record signing, eclipsing the £28 million they paid for Romelu Lukaku in 2014.
The fee is short of the £35 million Manchester City parted with earlier in the close-season to land Brazilian keeper Ederson, though Pickford would be the most expensive British goalkeeper ever.
That honour currently belongs to Southampton's Fraser Forster, who cost £10 million in 2014.