He was the eldest son of famed Russo-Japanese War general Kodama Gentarō, and his wife was the daughter of Prime Minister Terauchi Masatake.

After graduating from the Law School of Tokyo Imperial University in 1900, he obtained a position at the Ministry of Finance, passing his career civil service examinations the same year.

He was later assigned to serve in the Japanese Government-General of Korea, as a secretary to the Privy Council, and as a member of the House of Peers.

He visited Java in Japanese-occupied Netherlands East Indies as a special advisor in 1942 at the request of the Imperial Japanese Army.

After the surrender of Japan, Kodama was purged from public service by the Supreme Commander of the Allied Powers.