Sharecast - Matches offers more than 450 established and next-generation designers and generates the majority of its revenue internationally, with the business delivering to 150 countries outside the UK, Frasers said.
The gross assets of the acquired companies were around £170m at the end of January 2023.
Frasers (LON:FRAS) noted that the business has been loss-making in recent years and said the adjusted LBITDA for the year ended 31 January was a loss of £33.5m.
The company - which owns House of Fraser, Flannels and Jack Wills, among others - said the acquisition is an opportunity to further develop its Elevation Strategy and strengthen its luxury offering.
Chief executive Michael Murray said: "Matches has always been a leader in online luxury retail and has incredible relationships with its brand partners. This acquisition will strengthen Frasers' luxury offering, further deepening our relationships and accelerating our mission to provide consumers with access to the world's best brands.
"Whilst the global luxury environment is softer, we are confident that, by leveraging our industry-leading ecosystem, we will unlock synergies and drive profitable growth for Matches."