The decision comes after a review period where, for the first time, Kate Swann, the WH Smith chief executive, ordered an assessment of the retailer's entire range of titles.
WH Smith is holding discussions with publishers affected by the cuts, and the changes will take effect from 1 July.
Titles such as Prospect, the current affairs magazine, which is currently available in 175 WH Smith stores, will only be stocked in 41 under the new plan.
The move will see the creation of more space for big-selling consumer magazines and is in line with the system favoured by the supermarket chains, which only stock leading glossies.
WH Smith is the country's biggest magazine retailer and sells 40 per cent of paid-for magazines in Britain.
A WH Smith spokeswoman said: "Range reviews are a normal part of the business, ensuring that the magazines we stock reflect the current trends.
"We have to continually evaluate our offer, both to make sure that it is the best for our customers and also that it is commercially viable. Newspapers and magazines will remain a core category for WH Smith."
The Periodical Publishers Association has expressed concerns about WH Smith's wide-ranging review.
The chief executive at the PPA, Ian Locks, said: "WH Smith has, over many years, positioned itself as a destination range retailer. If by its actions it is jeopardising this position, then that would be highly regrettable."