John Clare, Dixons chief executive, described the deal as "a significant strategic step" and "a platform for growth". It is understood Dixons trumped an earlier pounds 350m offer from UK group Kingfisher.
Mr Clare said Dixons would focus on taking its computer retailing arm, PC World, to Scandinavia, and on strengthening the group's supply relationships across the region. Elkjop will continue its programme of increasing the number of its out-of-town stores.
There may also be opportunities to roll out Dixons' high-street brands and The Link mobile phone shops, said Mr Clare, although development plans for The Link would depend on what deals could be struck with Scandinavian mobile network providers.
The managements will also consider the enlarged group's position in Internet technology. Dixons owns Freeserve, andElkjop has a 22.5 per cent stake in Sense, a similar Internet service provider launched in Norway in August. Mr Clare said the groups will look at taking Freeserve's content partners to the Scandinavian market. Elkjop has a market share of about 12 per cent in Scandinavia, selling household appliances and consumer electronics from 154 stores.
Dixons will look at further opportunities to expand into Europe through acquisitions and joint ventures, but Mr Clare said targets would have to meet strict criteria: "They would have to be market dominant, with good management and prospects for growth." Major players in the French and German markets were "not available", he said. Elkjop was the largest company found so far which met Dixons' criteria.
The group said its move into Europe was not related to pressures in the UK market, including the arrival of Wal-Mart and the trend for supermarkets to sell electrical goods at discount prices. Mr Clare said: "These are separate challenges and opportunities that we are seeking to address."
The European retail industry is consolidating rapidly and UK companies are increasingly striking partnerships with foreign groups. Earlier this month Kingfisher bought Hugo van Praag, Belgium's second-largest electrical goods retailer. Sir Geoff Mulcahy, Kingfisher chief executive, last week said his company was aiming to make a German acquisition as part of its drive to boost its European presence.
Dixons yesterday built a 60 per cent stake in Elkjop, buying shares from management and some institutional investors. It offered 160 Norwegian crowns for each remaining share, a 7 per cent premium on Friday's price. The market reacted positively and Dixons' shares were up 61p at 1,341p yesterday.