Yūki was born in the onsen resort of Akayu in what is now part of Nan'yō, Yamagata Prefecture,[1] where his father was a sake brewer.

After graduating from Tokyo Imperial University with a degree in political science, he obtained a position at the Bank of Japan from January 1904.

In 1918, at the recommendation of Junnosuke Inoue, Yūki was appointed to the Board of Directors, while still maintaining his post as Osaka branch manager.

[4] Yūki was subsequently elected head of the Japan Chamber of Commerce and Industry in January 1937.

During the 1st Konoe administration, July 27, 1937 on Yūki returned to the Bank of Japan as governor, replacing Shigeaki Ikeda.