The Toffees had a bid for the 22-year-old right-back accepted last Thursday but manager Roberto Martinez admitted there was still a long way to go on the deal.
Byram was left out of Saturday's defeat at Sheffield Wednesday but, after discussing personal terms with Everton, the Hammers made their move and the lure of immediate first-team football - he would be behind Seamus Coleman at Everton - appears to have won them the race.
West Ham's offer is reportedly lower than the £3.7million, rising to £5million on the table from Everton.
"I'm really sorry for Everton because they really acted like gentlemen, but Sam chose West Ham," Leeds owner Massimo Cellino is quoted as saying in several national newspapers.