The Dundee-based company said shareholders had wanted changes to be made to improve performance.
Chief financial officer Alan Trotter is to leave Alliance Trust, while chief executive Katherine Garrett-Cox is to step down from the board.
The financial services company's share price rose when trading opened following the announcement.
Alliance Trust had been facing demands for a change in governance from US-based activist investor Elliott Advisers.
The firm aims to simplify its structures and reduce costs by £6m per year by the end of 2016, although details of staff cuts or other efficiency measures have not been announced.
Ms Garrett-Cox leaving the board means it now consists solely of non-executive directors, making it fully independent.
In a letter to shareholders, chairman Karin Forseke said the changes would take effect "as soon as practicable", and no later than March 2016.
She said: "The actions we have announced represent some of the biggest changes in our history, and are designed to further improve shareholder value.
"Implementation will require considerable further work by the team, but we believe that as a result Alliance Trust will be significantly better positioned for the future."
Managers at Alliance Trust, the venerable Dundee finance house, have been under siege for years. Having had to sue for peace earlier this year, the terms are now clearer, and they mean a radical change of direction.
A cut in costs of 20% will feel painful at the Tayside headquarters. Non-core assets are being sold,  and new benchmarks are being set, with regular overviews to check how management of the fund performs against the market.
They've been ahead of their benchmark since last year, but if they don't perform adequately in future, the board members brought on by activist investors will re-consider the decision not to contract out fund management to another company.
The scale of the change to the Trust's strategy, and the clipping of senior executives' influence, by removing them from the board, is such that you might expect the resignations of chief executive Katherine Garrett-Cox and/or chairwoman Karin Forseke.
However, this follows consultation with the full range of shareholders, and the long-term smaller ones may see the current bosses as their best protection against short-term profit-taking. With lead activist investor Elliot Advisers upping its stake recently, this is an uneasy-looking settlement.
Investment firm Alliance Trust is to cut costs by £6m while restructuring its board to become fully independent.