The £12.3m deal will see the UK department store take over the 141-year-old chain from Magillum.
Magasin du Nord operates six stores in Denmark, including a flagship store in Copenhagen. The business has a turnover of £229m.
Debenhams chief executive Rob Templeman says the deal will be “mutually beneficial” as there is a close fit between the two businesses. He added that the deal will be “highly accretive” for Debenhams’ shareholders.
He says: “The success of our international business demonstrates that there is demand for our own bought and Designer brands outside our home market which we believe will complement Magasin’s existing brands.”
Debenhams operates 157 UK stores and 52 franchise stores in 17 countries.
In October, Debenhams reported an increase in full-year profits, up 14% to £120.8m driven by the performance of its Designers at Debenhams range.
Debenhams is converting over 500,000 square feet of store space from concessions to own-bought ranges as part of a strategy to focus on Designers at Debenhams.