The online fashion specialist, which has already bought the Debenhams name amid the COVID-19 collapse for physical retailers, said it was to buy all the ecommerce and digital assets of the three brands, as well as their stock.
The deal does not include the retailers’ physical stores and the brands will become online-only.
All 214 Dorothy Perkins, Wallis and Burton stores will now permanently close, resulting in thousands of high street job losses.
In total, 260 employees from the design, buying, merchandising and digital teams will transfer to Boohoo.
Boohoo said the deal will grow its market share across a broader demographic, strengthen its menswear proposition and add new own-label brands for its Debenhams marketplace.
Boohoo chief executive John Lyttle said: “We are delighted to announce the acquisition of the assets associated with the online businesses of the three established brands Burton, Dorothy Perkins and Wallis.
“Acquiring these well-known brands in British fashion out of administration ensures their heritage is sustained, while our investment aims to transform them into brands that are fit for the current market environment.
“We have a successful track record of integrating British heritage fashion brands onto our proven multi-brand platform, and we are looking forward to bringing these brands on board.”
The collapse of Sir Philip Green’s Arcadia empire in December placed 13,000 jobs at risk and only a tiny fraction of 2,500 workers were understood to be saved when Boohoo rival ASOS landed the top names, including TopShop and Miss Selfridge, a week ago.