The Norwegian midfielder arrived on a free from Borussia Monchengladbach last summer on a five-year deal but now heads back to Germany.
Nordtveit is joining Hoffenheim for £1.5m after making just 11 starts in the Premier League.
Hammers boss Slaven Bilic said: “I would like to thank Havard for his commitment and hard work last season.
“He is an excellent professional and we wish him all the very best at Hoffenheim.”
Nordtveit’s exit less than a year after signing is evidence of their dismal work in the transfer market this time last year.
West Ham have already axed fellow flops Alvaro Arbeloa, Jonathan Calleri and Gokhan Tore.
Highly-rated teenage defender Reece Oxford is joining Monchengladbach on a season-loan loan.