Visa Inc. said Chief Executive Officer Charles Scharf is resigning after advising the board that he can no longer spend enough time in San Francisco “to do the job effectively.”

The San Francisco-based payments network said Mr. Scharf will be succeeded by Alfred Kelly, 58 years old, a member of Visa’s board and a former president at American Express Co. In an interview, Mr. Scharf said he needs be closer to his family in New York.

“I...