Henry signed for the Hammers from FC Toronto during the January transfer window, but his initial progress at the club has been hindered by injury.
However, Allardyce revealed on Friday that Henry is available for selection now and suggested that he would be in the squad to face West Bromwich Albion.
"Doneil Henry, who has been with us only a short time, is back fit," he said. "Mark Noble and Kevin Nolan are back with us. Overall it is still a very light squad. Guy Demel is back training. They could do with some more training but because we are where we are, they will go back into the squad."
West Ham have had to operate with a makeshift backline in their last two fixtures as the injuries have mounted, so reducing the numbers on the treatment table was crucial for Allardyce.
The Hammers will see their match with West Brom as an important one on Saturday, as the FA Cup offers them a good chance to win a trophy.
With West Ham's European push stalling somewhat in recent months, their best chance of success looks like it will come in the cup - with a number of the leading contenders already out.
The likes of Chelsea, Manchester City and Tottenham Hotspur have all exited at an early stage and West Ham may fancy their chances of going the distance, should they make it past Premier League rivals West Brom.