The 19-year-old son of former Chelsea man Gus Poyet, joins the club after his contract with Charlton expired.
The Hammers have agreed to pay Charlton an undisclosed compensation fee.
Speaking about the move, the youngster enthused, “I’m very happy to be here. It took me by surprise a little bit and it all happened very quickly. It’s a great Club to be at and I know a few of the boys here already.
“It was a no brainer to sign, I wanted to come out here to the training camp as soon as I could and I’m grateful that they’ve had me here.
“It’s massive to come to a Premier League club. It’s what I wanted to do - I wanted a new challenge and soon as I heard there was a chance of stepping up I had to take it.
“I played quite a few games last season with Charlton and I just want to push on now. Like any young player, the first thing you want to do is get into the first team. I need to show the staff, players and the gaffer what I’m capable of doing and maybe pushing my way in.
“West Ham is a great Club with a lot of tradition, moving to a new stadium and everything, it was a no brainer for me because you never know if you’re going to get that kind of chance again.”