Hydrogen gas undergoes a chemical reaction in which it is oxidized by oxygen; which itself is reduced by the hydrogen. In plain language, the reaction is that of hydrogen being burned and for which oxygen is required, just like in most other reactions where materials burn.
One molecule of water has two atoms of hydrogen and one atom of oxygen.
When hydrogen burns, the heat produced is sufficient to ensure that the end product is water vapor.
The balanced chemical reaction of the burning of hydrogen gas in the presence of oxygen is:
2H2 (g) + O2 (g) --> 2H2O (g)