The company named Alfred Kelly, Jr., a former president of American Express and a current Visa board member, as CEO. He will join the company on Oct. 31 as CEO designate.
"Charlie has been a visionary CEO, highly successful by any set of metrics," said Robert W. Matschullat, the company's independent chairman.
"He has helped transform Visa, the leading global payments technology company, into a technology-driven digital commerce company and has led a strategy that will benefit this company for years to come."
Kelly spent 23 years at American Express, and is the president and chief executive of the technology and media company Intersection. He also currently serves on the board of directors at MetLife.
CNBC's Jim Cramer obtained an internal Visa memo by Scharf to employees, where the chief executive says that the decision was entirely personal.
In it, Scharf said he has put Visa before "everything else," and needs to be on the East coast because of his wife and family in New York.
This confirms what Visa said in its press release about Scharf informing the board that he decided to resign because he could no longer spend the time in San Francisco necessary to do the job effectively.
During Scharf's tenure as CEO, Visa completed its acquisition of Visa Europe in June 2016 and increased its operating income to $9.1 billion (S$12.7 billion) in fiscal year 2015.
- Reuters contributed to this report