Deane, 35, made his last appearance in Wednesday's Carling Cup defeat at Aston Villa.
He becomes Alan Pardew's second signing for The Hammers, following Hayden Mullins from Crystal Palace.
"It is a good opportunity for Brian and I didn't want to stand in his way after the fine service he has given us," Leicester boss Micky Adams told the club's official website.
Deane's four seasons at The Whites totalled 161 appearances in all competitions and a less than staggering return of 38 goals.