The deal to form a minority cabinet gives Frederiksen a third consecutive term as prime minister, ending months of uncertainty after a March election in which 12 parties won seats in the Danish parliament.
"I have been to see His Majesty the King and announced that a government can be formed after long negotiations," Frederiksen told reporters.
Her centrist coalition lost its majority in the March 24 vote as Danes revolted over a cost-of-living crisis, although the Social Democratic Party remained the biggest group in parliament with 38 out of 179 seats, down from 50.
After more than two months of haggling, where the Social Democrats and the right-wing Liberals each sought to lead a new government, it was the 48-year-old Frederiksen who secured the necessary backing from parties in parliament.
"It is a government platform for the people who are in Denmark and for the generations to come and also for the animals," she said.
Animal welfare was one of several major topics debated in the election campaign.
The goverment's overall priorities will be presented on Tuesday while ministers will be named on Wednesday, Frederiksen said.
The government's immediate to-do list includes diplomatic talks over Greenland, which Trump has threatened to annex, and a rapid build-up of Denmark's military as security in Europe deteriorates amid Russia's war in Ukraine.
In addition to the Social Democrats, the new government will consist of the Social Liberals, the Left Greens and the centrist Moderates, relying primarily on the far-left Red-Green Alliance for a parliamentary majority, though it can also seek backing from other parties on individual votes.
The new government marks a shift to the left for Frederiksen, who in the past four years headed an unusual coalition across the left-right divide with her Social Democrats, the Moderates and the Liberals.
