"It's the happiest news a couple can ever have," he told a Danish TV station.
The 42-year-old, who is already father to three boys, said he was hoping for a daughter.
"Above all we hope that the baby is healthy and happy. That's the most important thing," said the royal, pictured with his wife and son Henrik at the family summer photocall.
But he added: "With regards to the sex - with three boys already I would like a little girl."
Marie is expected to give birth in Copenhagen University hospital in January.
The new arrival will be a little brother or sister for the couple's two-year-old Henrik.
He or she will also be a new half-sibling for Joachim's boys Felix, 12, and nine-year-old Nicolas – from Joachim's marriage to Alexandra, Countess of Frederiksborg.
With four children, the prince will be on equal footing to his brother Prince Frederik, also a father-of-four.
"It's a lot – if I look at the crown prince I can see it's a lot," he admitted. "However, it's a great blessing. It's marvellous."
The royal also said he wasn't worried about the age gap that will exist between the new baby and his elder children.
"I don't think it will be a great problem, said the proud dad. "The two elder boys are marvellous with their little brother and the other way around.
I can't see why it won't be the same with the fourth one.
Joachim's brother Frederik has also expressed his happiness about the announcement.
"It's brilliant news. We are so happy for them," the future king told magazine Billed-Bladet on behalf of him and his wife, Crown Princess Mary.