The online fashion retailer announced that it is buying Topshop, Topman, Miss Selfridge and HIIT.
Administrators for Sir Philip Green's retail group said Asos has paid an additional £65 million for current and pre-ordered stock.
Asos told investors on Monday morning that it will take on around 300 employees as part of the deal, which will not include any of the brands' stores.
At the start of December, Arcadia collapsed into insolvency after pandemic closures further provoked the group's troubles.
Last week, Boohoo said it was in exclusive talks to buy the Dorothy Perkins, Wallis and Burton brands in a move which will also not include any stores.
Asos said its acquisition of the four brands will "resonate" with its core customer base of "20-somethings" in the UK.
It expects the deal to complete later this week, adding that it will also see £20 million worth of one-off restructuring and transaction costs.
Asos chief executive Nick Beighton said: "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."