Hunt, who starts in the role tomorrow, succeeds Richard Larcombe, who left the bank in July to start his own business in the booming fintech sector.
Having spent more than 17 years with Barclays, Hunt has held positions including vice-president, UK banking, finance; marketing chief operating officer, global retail and business banking; and managing director, personal and corporate marketing, before moving to his current role in October 2015.
Larcombe joined Tesco Bank in December 2015 after six years at Virgin Media, where he was director of advertising and sponsorship, then chief marketing officer.
A Tesco Bank spokesman said: "Nigel joins with a wealth of experience in financial services. We look forward to Nigel supporting the growth of the Tesco Bank brand for Tesco shoppers."