The highly-rated 23-year-old has made 27 appearances for Pompey so far this season, but with financial worries looming over the club the move is part of exhaustive cost-cutting measures.
Henderson spoke of his delight at the short-term switch, and has immediately set his sights on displacing current Hammers No.1 Rob Green.
"As everybody knows, Portsmouth have financial difficulties, so I was told that West Ham put a bid in on Friday and that bid was accepted. I'm sad to leave Portsmouth but very happy to join a successful club in West Ham," the keeper told the club's official website.
"I'm aware that I might have to wait for my chance because Robert Green is one of the best goalkeepers in the Championship - everyone knows that. I will just come here, work as hard as I can and hopefully be ready when I'm given my chance.”
"I'm only 23 but I want to be playing games, like any other player. Robert Green is very respected but I'll keep working hard and we'll see what happens."