It is understood the Icelandic firm acquired its stake over the past few days, paying about 135p per share.
Speculation over a possible takeover of the department store chain arose yesterday when a dawn raid was conducted on the group's shares, sending prices up by 8.6 per cent.
The Icelandic group has expressed an interest in House of Fraser before. In 2002, along with retail entrepreneur Tom Hunter, it spent a year building a stake in the company before deciding against making a bid and sold its holdings.
Baugur has a strong presence on the UK high street. It owns names such as Oasis, Karen Millen and Hamleys. It also has a 10 per cent stake in Woolworths and a 14 per cent holding in fashion chain French Connection.
House of Fraser has recently been subject to takeover interest from private equity firm Apax, but talks between the two ended last month.
Baugur chief executive Jón Ásgeir Jóhannesson found out earlier this week that Iceland's special prosecutor would be resubmitting fraud charges against him, which were dismissed last year.
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