Set up in 1952, Jane Norman has 100 stores and concessions. It was bought by Graphite in 2003 for£70 million.
Corporate advisor Hawkpoint was appointed to organise the sale of the company. Baugur was one of several interested parties, including PPM Capital and Barclays Private Equity.
Baugur is expected to take between 30 per cent and 40 per cent of the equity in Jane Norman, while Kaupthing will take on equity and debt.
The deal is the first since Baugur announced that its chief executive Jón Ásgeir Jóhannesson was being investigated for fraud at the beginning of July.