TOKYO—Yasuhiro Nakasone, who survived combat as a World War II navy officer for Japan and boosted the nation’s postwar military and economy as one of its most influential prime ministers, died at a Tokyo hospital on Friday, according to his family. He was 101 years old.

Mr. Nakasone’s hawkish policies as prime minister from 1982 to 1987 and his push to solidify defense ties with the U.S. influenced the next generation of politicians in the ruling Liberal Democratic Party, including Japan’s current prime minister, Shinzo Abe....