Pearson, the publishing and media group and owner of the Financial Times, introduced the programme after the newspaper had been steadily losing money for two-and-a-half years. It only broke even in the fourth quarter of 2004.
The job cuts will include writers on the Saturday magazine as well as senior editors and sub-editors. Cartoonist Roger Beale is also set to leave.
The FT said that many of those deciding to leave will take early retirement.
The last time the FT made editorial redundancies was in 2001, when 20 staff departed in a similar voluntary scheme.
The paper made a £32m loss in 2003, although Pearson expects to reduce that by £20m this year.
A saving of £400,000 could be made by closing the FT's media supplement Creative Business, which has already been scaled back from a weekly to a monthly offering inside the main paper, following weak advertising.
Other cost-cutting initiatives introduced last year include stopping the paper's daily sports page and cracking down on company expenses.
The news comes as Peter Jovanovich, chief executive of Pearson Education and a board member, has announced he is stepping down for health reasons.
Jovanovich, 55, joined Pearson in 1997 to run Addison Wesley Longman. He had only recently returned to work after a double lung transplant.
The divisional presidents of Pearson Education will report to group chief executive Dame Marjorie Scardino.
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