Nordtveit will join the Hammers on a free transfer on July 1, the Premier League club have announced.
The Norway international has signed a five-year contract with West Ham.
He told the club’s official Website: “It has always been a dream for me to play in the Premier League and now I have a big opportunity to do that for West Ham – I cannot wait to start!
“This team has something special, a spirit in the team that I can fit into. I will work hard and hopefully I can get some good moments at this Club.
“I’m a player who can play many roles on the pitch, but I’m from Norway so maybe a little bit more running, tackles and try to spread a few balls around me.
“I’m looking forward to showing what I can do, but hopefully I have something to help West Ham achieve even more.”
Nordtveit joins on a free transfer on a five-year deal following his departure from @borussia_en #HavardIsAHammer pic.twitter.com/NkNNRI2AmA
— West Ham United FC (@whufc_official) May 16, 2016
