From Japanese 万歳(ばんざい) (banzai, “long live..., huzzah, hurrah”), from Middle Chinese 萬歲 (mjonᴴ sjwejᴴ), from Old Chinese 萬歲 (*mans s-qʷʰats, “10,000 years [of life]”, i.e. “immortality”), from 萬 /万 (wàn, “10,000”) 歲 /岁 (suì, “year (of age)”).
Compare Mandarin 萬歲/万岁 (wànsùi).