The Soham-born shot-stopper, who has played eight times for his country, had spent the past six seasons at Turf Moor, twice winning Burnley's player of the year award and helping the Clarets to qualify for Europe in 2017/18.
The Whites have beaten off competition for the 24-year-old, who will join for an undisclosed fee and has accepted terms on a five-year-contract at Elland Road.