Garrett-Cox will leave ATI on 11 March after months of discussion around her future at the company. It follows a major strategic review, which has already seen her step down from the board, after a showdown with activist investors Elliott Advisors.
Her responsibilities will be reassigned throughout the management team.
Investment responsibilities will be led by Peter Michaelis and the team who joined ATI in 2012 and have been managing the trust's equity portfolio since October 2014. Operational responsibilities will be passed to Ramsay Urquhart as managing director of ATI.
Chairman Lord Smith of Kelvin said: "Alliance Trust is undergoing significant change to improve both its operating performance and investment returns. It has always had investment expertise at its heart and Katherine has done much, over the past nine years, to refocus the investment portfolio on its traditional strengths in global equities.
"Alliance Trust is now moving swiftly to implement the changes announced last year which are designed to enhance shareholder returns. This process is well underway and it is clear to us all that the role of Chief Executive of Alliance Trust Investments has changed significantly. I and the rest of the Board wish Katherine every success in the future."
Garrett-Cox, who has been at the business since 2007 - first as chief investment officer, and then as chief executive, added: "It has been an honour to have had the opportunity to represent and protect the long-term interests of so many shareholders and to have been a guardian of the trust's historic purpose of investing for generations.
"I leave Alliance Trust Investments with a strong team who are already delivering improved investment returns and driving down costs."
Alliance Trust's share price was up 1.2 per cent in early morning trading.