The abdication ceremony took place at the royal Christiansborg Palace in Copenhagen earlier in the day and was broadcast by the DR television channel.
The Danish Defense Ministry announced later in the day that King Frederik X had been awarded the ranks of admiral of the fleet and general of the ground and air forces on the occasion of the transfer of the throne to a new monarch.
The ministry also said that the new Danish ruler had "extensive military experience", military education and served in the various branches of the country's armed forces.
Queen Margrethe II announced in her New Year's address that she would abdicate the throne on January 14, when her reign reaches 52 years. The 83-year-old monarch said she would leave the throne to her eldest son, Crown Prince Frederik.
She was Denmark's ruler longer than all her predecessors in the entire history of the country.