Crown Princess Mary of Denmark has given birth to a healthy boy and girl at a Copenhagen hospital.

The births, which came on Saturday morning local time at Rigshospitalet, had been much anticipated.

A relieved Crown Prince Frederick fronted local and international media gathered at the hospital just after 11:30am (9:30pm AEDT).

"It's a happy occasion to announce that Crown Princess Mary has given birth to perfectly healthy babies," Crown Prince Frederik said.

"A boy and then a girl right after."

He added the entire royal family had known the sex of the twins before the birth.

The future king of Denmark was pleased to announce that Tasmanian-born Princess Mary, 38, had also come through the birth without any issues.

"She handled it beautifully," he said.

"Both mother and children are doing well and we are very happy."

The boy, weighing 2674 grams and measuring 47cm, was born at 10:30am (local time) and the girl just under half-an-hour later. She weighed 2554 grams and measured 46cm.

Crown Prince Frederik said he had already called his mother, Queen Margrethe II, to tell her the news.

"The Queen was totally happy when I rang her," he said.

A team of two doctors and three midwives had been on hand since 6:00am local time to handle the birth.

Team leader Morten Hedegaard told the waiting media that his team was thrilled with the result.

"They cannot be better," he said.

Princess Mary and her husband already have two children - Prince Christian, five, and Princess Isabella, three.

The royal couple met at the Olympics Games in Sydney in 2000 and were married four years later in Copenhagen.

Crown Prince Frederik is first in line to suceed Queen Margrethe II, who has reigned since 1972.

- ABC/AAP