Fullkrug was on the London club's radar before last season but chose to move from Werder Bremen to fellow Bundesliga club Dortmund, where he scored 16 times in 46 appearances across all competitions.
"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," Fullkrug said.
"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 financial details of the deal were not disclosed but the Hammers reportedly paid 27 million pounds ($34.5 million) for the German international.
Fullkrug was in Germany's EURO 2024 squad, scoring twice in five matches.
