The fast-food brand, owned by South African firm Famous Brands, is to remove a series of long-established desserts, such as the Knickerbocker Glory and Banana Longboat, from its menu.
However, Wimpy is to retain its famous Bender in a Bun - a curled sausage served in a roll - despite the changes.
The revamped menu will be rolled out in UK restaurants on 23 May, supported by digital marketing activity.
According to Wimpy's UK marketing manager, Clare Starling, the overhaul marks the biggest change to its dessert menu since the late-80s.
Several desserts, including Cheese Cake, Deep Filled Apple Tart and Choc Fudge Cake, have been deemed 'outdated', though Wimpy will continue to offer the Brown Derby, a doughnut topped with a scoop of vanilla ice-cream.
Additions to the menu will include an Eskimo Waffle - ice cream sandwiched between two Belgian-style waffles and topped with cream and maple syrup.
Wimpy is also trialling some savoury products, such as a line of 'open burgers' with a range of fillings.
These include a Brunch Burger, a quarter-pounder with egg and bacon, and a Mushroom Burger featuring grated cheddar, griddled mushrooms and a beefburger.
The brand, which, unlike McDonald's and Burger King, serves food on plates, is also refreshing the design of its menus (above). Starling said Wimpy had decided to 'radically' cut the number of pages and pictures to make menus easier for customers to navigate.
In 2008, Wimpy introduced a US diner-style format to its branches. Restaurants were redecorated using a silver and red colour scheme, replacing the traditional red and yellow fascia.
Wimpy opened its first restaurant in London in 1954. At its peak in the 70s, it operated thousands of outlets across more than 20 countries.