Byram had been expected to join Everton, and the Italian owner has expressed his sympathy for the Merseyside club, who had a bid accepted by Leeds on Thursday night.
Massimo Cellino is quoted: “I’m really sorry for Everton because they really acted like gentlemen, but Sam chose West Ham."
The news is potentially even more disappointing for Leeds, with The Guardian reporting West Ham have offered less money than the fee proposed by Everton.
Leeds' hand has been forced by their inability to tie Byram down to a new contract, with his current deal set to expire this summer.
Byram has been with Leeds all his career to date, but the lure of regular Premier League football is evidently a strong one.
The 22-year-old has been in and out of the Leeds team this season, playing in both defence and midfield, and won the league's Player of the Month Award in December after scoring three goals and setting up another.
Leeds are currently in 17th place in the Championship after losing to Sheffield Wednesday at the weekend, in a match where Byram did not feature.