Shares fell 8% in after market trading.
Peck, who is president of the Growth, Innovation and Digital division, will succeed current CEO Glenn Murphy on February 1, the company said in a statement.
Murphy is retiring after seven years on the job, according to the release.
Peck has worked at Gap since 2005, and is credited with creating the digital business.
""I'm honored to be given the opportunity to lead this company with such powerful brands and incredible talent - a combination that sets us apart globally," Peck said in the release.