The book has come as a surprise to Danes, and media outlets have been hastily live-blogging lines from it.
“The King’s Word” promises Frederik’s thoughts on topics including Denmark’s place in the world and his relationship with his wife, Queen Mary.
Frederik was crowned king on Sunday after his mother, Margrethe II, abdicated on New Year’s Eve.
The book costs up to 250 Danish Krone (£29; €33.50) and is around 110 pages long.
It was written with Jens Andersen, who authored Frederik’s 2017 biography, and is based on interviews conducted over the last year-and-a-half.
In one section, Frederik says that, as a child, he had difficulty accepting he would become King of Denmark, saying he “just wanted to be like all other boys of my age”.
“I remember my 18th birthday as something similar to the end of the world. It was the feeling that now everything that was fun and exciting was coming to an end. Fortunately, it didn’t,” Frederik says.
Later in the book, the king also reportedly discusses his faith, saying that he and his Australian-born wife say prayers with their children every evening.
He also talks about family life, saying that his father – the late Prince Henrik of Denmark, who died in 2018 – was “very patriarchal” and “tried to pass that pattern on to his two sons”.
Frederik says: “I have learned a lot from having a wife who, from time to time, reminds me that of course I am not always right, and that my words are not automatically believed, just because I am a man in the house.”
Tens of thousands of people turned out to watch King Frederik X succeed his mother as the monarch of Denmark on Sunday.
Blinking back tears, Frederik told a cheering crowd outside Christiansborg Castle in Copenhagen that he hoped to become “a unifying king” for the future.
His mother, Margarethe II, abdicated after 52 years on the throne.
