She will join the board on 1 March and become chairman on 2 April, following a handover period with current chairman Lesley Knox.
Ms Knox is retiring from the Board after eleven years, having been appointed as chairman in 2004.
Ms Forseke currently works as deputy chairman and senior independent director of the FSA and as a non-executive director of Swedish shipping company Wallenius Lines and the Royal Opera in Stockholm.
Previously she has worked as chief executive of Swedish investment bank D Carnegie & Co AB and as chief operating officer of the London International Financial Futures and Options Exchange.
She has also extensive political experience, having spent time as a board member of the European Council on Foreign Relations and as private advisor to the Minister of Financial Markets.
Ms Knox said: “I am delighted to welcome Karin Forseke as the next chairman of Alliance Trust. She has extensive experience of financial services and this, alongside her international perspective, will be invaluable as we continue to invest across the globe in order to seek value for our shareholders.”