The 31-year-old has agreed a four-year contract at the London Stadium for a fee understood to be around $53m, becoming the fifth summer signing brought in by new Hammers boss Julen Lopetegui.
"I'm delighted to be here, and I can't wait to get out on the pitch with my new team-mates," Fullkrug said.
"I think the Premier League is the best league in the world, and for me it is the right time to move over to England and play for a big club like West Ham.
"I have been thinking about West Ham for a long time now - I know the technical director Tim Steidten very well, because we have history at Werder Bremen together, and I have watched some games and seen how much quality there is in the team.
"The chance to play under the head coach is also really exciting. His playing style is important for me, and I am confident that under him I will be able to perform at my best, and score lots of goals."
Fullkrug scored 16 goals in 46 appearances for Dortmund last season, helping them reach the Champions League final which they lost to Real Madrid.
Lopetegui has also signed winger Crysencio Summerville from Leeds and defender Max Kilman from Wolves, as well as goalkeeper Wes Foderingham and Brazilian winger Luis Guilherme.
The Hammers are also close to completing the free-transfer signing of Argentina midfielder Guido Rodriguez.
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