The images, which include a joint photo of the couple as well as solo shots, show Mary wearing the crown jewels, reports news.com.au. They were taken at Christiansborg Palace in Copenhagen.
The royal couple also wear the Order of the Elephant on chains around their shoulders in the portraits, which will be shown in state institutions all over the world.
The couple became the country’s King and Queen in January, when Queen Margrethe II announced her shock abdication during her New Year’s Eve address.
The Queen made a bold statement last week during an official engagement, as she wore a necklace with a letter F pendant, presumably for Frederik.
Rumours about the state of their marriage began circulating when Spanish magazine Lecturas published images of Frederik during a night out with socialite Genoveve Casanova in November.
According to the magazine, the royal and Casanova went to a Picasso exhibition, went out for dinner and walked around a park together.
The outlet reported that the pair both headed to her apartment separately, leaving the building two hours later.
Asked about the allegations, the palace refused to make a statement, explaining that it “never comments on rumours” - but Casanova herself shared a statement with media.
“I flatly deny the statements that suggest a romantic relationship between Prince Frederik and me,” she told Hola at the time.
“Any statement of this type is not only completely untrue but also distorts the facts in a malicious manner.”
The royal couple tied the knot in 2004 and have four children together - Prince Christian, 18, Princess Isabella, 16, and twins Prince Vincent and Princess Josephine, 12.