Fuellkrug scored 16 goals in his sole season at Dortmund to help the German giants reach last season's Champions League final.
The 31-year-old also netted twice despite starting all five matches on the bench as Germany reached the quarter-finals of Euro 2024 on home soil.
A battering ram of a centre-forward, Fuellkrug is a huge fan favourite in his homeland, with many calling for him to start ahead of Arsenal's Kai Havertz at the Euros.
"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," said Fuellkrug in a club statement.
West Ham have been one of the busier Premier League sides during a quiet transfer window so far.
Wingers Crysencio Summerville and Luis Guilherme and defender Max Kilman have also joined the 2023 Europa Conference League winners for Julen Lopetegui's first season in charge.
"We are delighted to have signed Niclas," said West Ham technical director Tim Steidten, who previously worked with Fuellkrug at Werder Bremen.
"I have worked with him previously and I know what he will bring to us in terms of his physical and finishing qualities, as well as his character and mentality."
