The attacker had an outstanding season in the Bundesliga and an impressive Euro 2024.
Hannover-born Füllkrug was welcomed to the club by their technical director Tim Steidten.
“We are delighted to have signed Niclas,” said Steidten to club media.
“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.
“He has enjoyed a really positive last couple of seasons, both at club level, where he played in the Champions League final last season, and with Germany at the Euros this summer, and he joins us with a clear desire to build upon that progress and prove himself in the Premier League.
“Niclas has great experience and is at the stage of his career where we feel he can really give us his best years. He is someone who we have watched very closely, and who we believe will be an excellent fit for the team and for the Club. We look forward to seeing the qualities he will bring.
“The Board continue to show their backing by bringing in top-class players to strengthen the squad at West Ham United.”