The court ordered the widow, children and grandchild of Mario Ovando, who lived in the port city of Talcahuano in Concepcion province, be paid about $100,000, the BBC reported.
The court was told following the earthquake, Ovando heard a radio announcement that there was no danger of a tsunami and decided to remain in his home. Twenty minutes later his house was swallowed up by huge waves. His relatives freed him and took him to a hospital, but Ovando died three days later.
More than 500 people died in the February 2010 earthquake and the tsunami that followed. Coastal villages were hit by huge waves after the government lifted an initial tsunami warning.
The Chilean Navy, which runs the Hydrographic and Oceanographic Service, admitted it erred in its analysis and provided unclear information to government officials, who issued an alert, deactivated it and then reissued it once the waves struck.
Many families of victims have filed lawsuits against the Chilean province, claiming the misinformation led to wrong decisions, the BBC said.
The earthquake and tsunami left more than 800,000 people homeless.