However, it does not include the brands' 214 remaining shops, which will close, according to administrators from Deloitte.
Around 260 jobs, mainly head office roles, will be saved as they move with the brands to Boohoo, including jobs in design, buying and merchandising, and the businesses' digital wings. Some other staff will be kept on during a months-long transition period, Deloitte said.
The deal will see the brands transfer over to online fashion giant Boohoo, which said it had bought the brand and website of department store chain Debenhams for £55m last month. It did not take on the company's 118 stores, meaning the likely loss of around 12,000 jobs.
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 on to our proven multi-brand platform, and we are looking forward to bringing these brands on board."
Boohoo chairman Mahmud Kamani added: "This is a great acquisition for the group as we extend our market share across a broader demographic, capitalising on growth opportunities as more and more customers shop online.
"We continue to grow our portfolio of brands and customer base, strengthening our position as a leader in global fashion e-commerce."
Arcadia was formerly one of the most significant retail empires on the UK high street, but the coronavirus pandemic dealt the final blow to the business, which had been struggling with a shift in shopping behaviour in recent years.
In December it entered administration, putting thousands of jobs at risk.
While the business's demise has been partly brought about by a shift to online retail, its brands will now continue to live online, after several deals.
Last week Boohoo's rival Asos, also an online player, signed a £330m deal to buy Topshop, Topman, Miss Selfridge and HIIT from Arcadia.
Administrators have now sold all of Arcadia's brands, raising around £500m to pay off creditors. There is still some property in the portfolio left to sell.
Additional reporting by Press Association
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies