The Oxygen Destroyer works. Godzilla rises to the surface and screams in pain, but quickly dies and sinks back into the ocean. His bones remain on the ocean floor because sequel.
Fun fact: That's no joke. The Godzilla skeleton from this movie return in 2002's Godzilla Against MechaGodzilla. In the film, scientists use the skeleton to create MechaGodzilla to fight against a new Godzilla, but the spirit of the old Godzilla eventually poses MechaGodzilla and it rampages hard. This probably goes without saying, but things got weird in the Godzilla franchise. (Source)
The newscasters announce victory, and everyone cheers except Ogata and Emiko, who are overwhelmed with grief at Serizawa's sacrifice.
Yamane stares at the ocean and ponders to himself that another Godzilla may appear someday as long as nuclear testing continues. (Dude has no idea.)
The crew of the ship present arms in respect of Serizawa, and the movie closes with a shot of the sun setting over the vast ocean.