The Icelandic investor is expected to merge the 32 Mappin & Webb and Watches of Switzerland stores with UK high street jeweller Goldsmiths, which Baugur bought 18 months ago.
Gunnar Sigurdsson, Baugur managing director of UK investments, said: 'We regard the acquisition of Mappin & Webb, with its excellent brand and reputation, as a significant opportunity to strengthen Goldsmiths' position in the high-end jewellery market.'
Mappin & Webb chief executive Nick Evans said: 'We are very pleased with this deal, which we believe gives both companies increased strength. Our priority is to focus on the Christmas season before starting to look at integration with Goldsmiths.'
Baugur said it would keep the brands separate as it moves forward with a high street empire of more than 200 jewellery shops across the UK. Baugur also controls retailers including Hamleys, Oasis and Karen Millen.
Mappin & Webb was founded in 1774 and holds two royal warrants, as silversmith to the Queen and the Prince of Wales.