A row of monks bowed to the couple as they arrived at the Tashichho Dzong fortress in the capital Thimphu for a private audience with King Jigme Khesar Namgyel Wangchuck and Queen Jetsun Pema.
The Duke and Duchess of Cambridge flew into the picturesque mountain kingdom on Thursday morning from India, where they played cricket, hung out with top Bollywood actors and laid a wreath at a memorial to India's war dead.
Bhutan's Oxford-educated monarch -- known as the Dragon King -- greeted the British couple in Bhutanese national dress, which is still required to be worn in schools and the workplace.
His wife also wore traditional dress, while Catherine, Duchess of Cambridge, wore a black and cream cape top and a long blue printed skirt reportedly made from fabric hand-woven in Bhutan.
Also Read
King Jigme came to the throne in 2006 after his father abdicated and agreed to cede absolute power to a parliamentary democracy.
After their meeting, William and Kate will head to an open-air archery venue to watch the national sport as well as other traditional games.
Bhutanese archers must aim at very small, brightly decorated wooden targets positioned 145 metres (475 feet) away from where they are standing.
Later the couple will have a private dinner with Bhutan's king and queen.
Tomorrow, they will take a six-hour trek to Paro Taktsang, a spectacular Buddhist monastery perched on a cliff edge.