The investment trust confirmed it will create a wholly independent board as part of changes to its governance structure, which aim to improve performance.
Senior independent director Alastair Kerr will also stand down from the board on January 1, earlier than his previously-announced May 2016 departure.
Karl Sternberg will assume the role of senior independent director from January 1 and will lead the search for an external candidate to replace Ms Forseke.
Gregor Stewart, a non-executive director of Alliance Trust since December 2014, has been named interim chair.
Ms Forseke said: “We are making good progress implementing the changes announced in October to accelerate our long-term strategy and we expect the new governance structure to be in place in early 2016. Alongside the new non-executive only board of the trust, excellent independent boards will be in place to oversee the development of Alliance Trust Investments and Alliance Trust Savings.
“As these changes are implemented, the chair of the trust’s role will change and as a result I believe now is the right time for me to move on.”
Mr Kerr added: “We have set out the strategy for Alliance Trust and I am confident that the new structure will allow it to flourish. I had planned to stand down in May 2016, but I feel that the new team should be responsible for identifying Karin’s successor, and standing down at this time will ensure a smooth transition.”
He acknowledged it had been a “challenging period” for the trust, which came under pressure from activist investor Elliott Advisors earlier this year for its underperformance.