Arnold, who has been a board member for 14 years, will succeed Bob Iger on Dec. 31.
Iger, who stepped down as Disney's chief executive officer in 2020 after 15 years in the role, will leave the company by the end of this month.
Arnold's appointment comes at a time when big corporations are moving away from an organizational structure where the CEO and chairperson roles are held by a single person following a push by corporate-governance experts, shareholders and, in some cases, regulators to untangle the two roles.
Arnold was formerly an operating executive of the equity investment firm The Carlyle Group. She has also served in executive roles at Procter and Gamble and McDonald's Corp.