Each group would hold 50 percent in a joint venture that would have a 40 percent market share and annual revenue of over nine billion kroner ($1.5 billion), the two companies said.
"The need for consolidation in the Danish telecom market has been apparent for a while as operators face continued pressure on revenues and profitability, limiting the room for investments and innovation," Telenor said in a statement.
The Nordic countries have some of the world's most mature telecom markets, and Denmark last week overtook South Korea as the world's most connected country in the International Telecommunications Union's ICT development index.
The survey takes into account Internet and mobile phone access and use, and the population's competence with the technology.
The merger would create Denmark's biggest mobile carrier by number of customers, just ahead of incumbent TDC, which holds a 39 percent market share.
Denmark has long been a weak spot for the otherwise profitable Telenor, racking up an operating loss of 86 million Norwegian kroner ($12.2 million) in the first nine months of the year.
TeliaSonera said the deal would create "significant synergy potential".
The transaction required approval from the EU Commission and was expected to close in 2015, the companies said.
In Norway, another mature market, TeliaSonera continues to compete with Telenor and has sought to buy the assets of Sweden's Tele2, but the country's competition watchdog has said it may block the deal, which would give the new group a 40 percent market share.
Telenor and Sweden's Telia aborted a merger in 1999 after disagreement over, among other issues, where to base the group's head office for mobile telephony, prompting the Swedish communications minister to accuse Norway of being "the last Soviet state".