The search was funded by Microsoft co-founder Paul Allen.
Hawking died on Tuesday at 76 years old.
"As Americans, all of us owe a debt of gratitude to everyone who served and who continue to serve our country for their courage, persistence and sacrifice."
The warship was torpedoed by the Japanese during World War II, and for 72 years, its whereabouts remained a mystery.
It was 18,000 feet under the water's surface.