Philip Green's Arcadia Group collapsed into administration in November last year, putting 13,000 jobs at risk.
Asos has however not agreed to buy the four brands' 70 stores, putting the jobs of 2,500 high street retail workers in question. Only 300 head office staff will be saved as part of the deal, to help Asos with design, buying and retail partnerships.
Arcadia Group as a whole had 500 stores across the UK when it entered administration.
Asos is paying £265m for the brands and £30m for stock.
Asos described the deal as a compelling strategic opportunity in support of its mission to become the number one destination for fashion-loving 20-somethings worldwide.
"These are strong brands that resonate well with our core customer base. Brand equity is strongest in the UK and they have an established presence in both the US and Germany, two of our key strategic markets. The Asos multi-brand model has our Asos brands at the core, supplemented by a curated edit of the best product from the most relevant brands globally. This transaction allows us to bring iconic brands in-house, allowing us to overlay our core strengths and transform them into leading digital first brands," said Asos.
Nick Beighton, Asos CEO, commented: "We are extremely proud to be the new owners of the Topshop, Topman, Miss Selfridge and HIIT brands. The acquisition of these iconic British brands is a hugely exciting moment for Asos and our customers and will help accelerate our multi-brand platform strategy.
"We have been central to driving their recent growth online and, under our ownership, we will develop them further, using our design, marketing, technology and logistics expertise, and working closely with key strategic retail partners in the UK and around the world."
The transaction is expected to be finalised later this week.
