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The Toffees have paid an undisclosed fee, reportedly in the region of £12m, to convince the Swans to part company with their long-serving centre-back.
Williams joined Swansea from Stockport County in a £300,000 deal in March 2008. He clocked up more than 300 appearances for the Welsh club during his eight-year stint with them.
He starred for Wales in their run to the semi-finals of Euro 2016 and has not featured at all in pre-season due to an extended break after the tournament.
Everton sold centre-back John Stones to Manchester City yesterday, so Williams effectively arrives on Merseyside to replace him in Ronald Koeman’s squad.
Swansea had earlier rejected a £10m bid from Everton for Williams, who is said to have then submitted a transfer request that was accepted by the Liberty Stadium hierarchy out of respect for his service to the club.
