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.

Those selling the illicit weapons often disassembled and sent them in different packages or embedded them in old stereos or printers, the report found.
Researchers found that firearms and related goods generated 136 sales per month and a monthly revenue of $80,000 (Â£62,000).
The firearms trade has gained attention following recent terrorist attacks.
The dark net is a part of the internet that requires specific software to access, in order for users to remain anonymous.
While the trade was unlikely to fuel large-scale terrorist operations, it had the potential to become the platform of choice for "lone-wolf" terrorists to obtain weapons and ammunition, the report said.
Non-profit organisation Rand Corporation Europe, working with Manchester University, found 52 unique vendors selling weapons or similar items such as ammunition, explosives, or components such as silencers across 811 listings and 18 markets.
Police believe the 2016 Munich shooting, which left nine people dead, used weapons purchased on the dark net.
Lead author of the research, Giacomo Persi Paoli, said: "Recent high-profile cases have shown that the threat posed by individuals or small groups obtaining weapons illegally from the dark web is real.
"The ability to not only arm criminals and terrorists, who can make virtually anonymous purchases, but also vulnerable and fixated individuals is perhaps the most dangerous aspect."
Guns account for less than 1% of items sold on the platform, with its main trade being in narcotics.
Nevertheless, the volume being sold "can be considered sufficiently high to be a cause of concern for policy makers and law enforcement agencies", said the report.
The study involved collecting data from 12 dark net marketplaces during a week in September 2016.
Most of those selling guns were based in the US, but Europe was the most popular destination for the weapons they sold.
Judith Aldridge, co-investigator on the study, said: "In very simple terms, anyone can connect to the dark web and within minutes have access to a variety of vendors offering their products, which are most often illegal.
"The dark web enables illegal trade at a global level, removing some of the geographical barriers between vendors and buyers, while increasing the personal safety of both buyers and sellers through a series of anonymising features that obscure their identities."
Investment firm Alliance Trust is to cut costs by £6m while restructuring its board to become fully independent.
[NEXT_CONCEPT]
Criminals and terrorists are using the so-called dark net to buy weapons, a new study has suggested.