Social Democrat Frederiksen will lead a new centre-left government consisting of four parties, the DPA reported.
Late on Monday, Frederiksen informed King Frederik X of her intention to form a coalition made up of her Social Democrats, the Socialist People's Party, the right-wing liberal Venstre party and the centrist Moderates.
"His Majesty the King has subsequently invited acting Prime Minister Mette Frederiksen to form such a government," read a statement from the Danish Royal House.
The four parties combined hold 82 seats in the Danish parliament, short of the 90 required for a majority.
Although minority governments are common in Denmark, a governing coalition must avoid facing a majority opposition in parliament. To ensure this, the new government needs the support of, for example, the eleven seats held by the left-wing Red-Green Alliance. The party announced on Facebook on Monday night that it would have "big news for Denmark tomorrow."
This is Frederiksen's third term, following her wins in 2019 and 2022. She had previously lost the mandate to form a new government after failing to reach a coalition deal despite weeks of negotiations.
The leader of the right-wing liberal Venstre party, Troels Lund Poulsen, was then given a chance to form a government but his efforts also failed. Frederiksen has been back in charge for just over a week.
Former Danish prime minister, and current foreign minister, Lars Løkke Rasmussen and his centrist Moderates once again played a crucial role in the government negotiations. Rasmussen spoke with both sides and broke off negotiations twice.