He succeeds his mother, Queen Margrethe II, who formally abdicated after 52 years as monarch.
Eighty-three-year-old Margrethe stunned the nation on New Year's Eve when she announced she would become the first Danish monarch in almost 900 years to voluntarily relinquish the throne.
In attendance Sunday were Margrethe, Frederik, his Australian-born wife Mary, who is now queen, and their oldest son Christian, 18, who is the new heir to the throne.
Denmark has one of the oldest monarchies in the world.
Tens of thousands from all over Denmark braved the cold for the event - a sign of the popularity the monarchy enjoys in the nation of nearly six million.
"I think the event was good. It's going to be interesting to see how he's going to cope being a king. It's a big change for him, but it's also a big change for the Danish people. We are used to having a queen."
"Ah that was emotional because, you know, after - I'm 52 years old and she's been a part of my life, the whole life you know, and the way she has performed is outstanding, I must say."
The couple will continue to reside with Margrethe, who will retain her title as queen, in their respective palaces at the Amalienborg royal complex.
A recent survey indicated that 82% of Danes expect Frederik to do well or very well in his new role, while 86% said the same about Mary.
