The 19-year-old, son of Sunderland head coach Gus Poyet, turned down a new contract with Charlton last month and West Ham will pay an undisclosed compensation fee to the Championship side.
Zaragoza-born Poyet, who came through the academy at The Valley and made 23 appearances for the club, had been linked with Manchester City and Chelsea.
The teenager has already linked up with his team-mates in a pre-season training camp on the France-Switzerland border and is in no doubt that he has made the right choice.
"I'm very happy to be here. It took me by surprise a little bit and it all happened very quickly," he told the club's official website. "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."
Poyet, who made six appearances for England at Under-17 level, is the London club's fourth signing ahead of the 2014/15 season after Sam Allardyce recruited Mauro Zarate, Cheikhou Kouyate and Aaron Cresswell.
