William spoke with the First Minister of Wales on Sunday, thanking him for his “fitting tribute” to his grandmother, the Queen, following her death.
He revealed in the telephone conversation that he would be travelling to the country “at the earliest opportunity” to meet Mark Drakeford and other political leaders in person.
A statement released by Kensington Palace said: “HRH expressed his and The Princess of Wales’s honour in being asked by His Majesty The King to serve the Welsh people.
“They will do so with humility and great respect.
“The prince acknowledged his and the princess’s deep affection for Wales, having made their first family home in Anglesey including during the earliest months of Prince George’s life.
“The prince and princess will spend the months and years ahead deepening their relationship with communities across Wales.
“They want to do their part to support the aspirations of the Welsh people and to shine a spotlight on both the challenges and opportunities in front of them.
“The prince and princess look forward to celebrating Wales’ proud history and traditions as well as a future that is full of promise.
“They will seek to live up to the proud contribution that members of the royal family have made in years past.”
The former prince of Wales ascended to the throne following the death of his mother, Queen Elizabeth II, on Thursday.
Charles was created the Prince of Wales by the Queen when he was just nine years old, with the title belonging to him for more than 64 years.
The title Prince of Wales has long been used for heirs to the throne but it is not an automatic right and is the choice of the sovereign to award it.
William and Kate became the new Prince and Princess of Wales, with the King announcing their titles in his historic address to the nation on Friday.
Kate has become the first person since Diana, Princess of Wales to use the title.
Thousands of people gathered at Cardiff Castle to hear Charles be proclaimed King in Wales.
More than 2,000 were allowed inside the grounds but hundreds more lined the street outside the castle walls, including two protesters holding signs reading: “Not our king!”
Charles was formally proclaimed King at a historic ceremony in St James’s Palace in London on Saturday following a meeting of the Accession Council during which he swore an oath to privy counsellors.
Proclamations were then read out across the UK the next day, including Wales, at midday.
Prior to the proclamation, 26 men of the 3rd Battalion the Royal Welsh – supported by the Band of the Royal Welsh – marched from City Hall at 11.25am along the Boulevard de Nantes, North Road and Duke Street to the castle.
They were accompanied by the regimental mascot, a Welsh billy goat called Lance Corporal Shenkin IV, and Goat Major Sergeant Mark Jackson.
Inside the castle, Mr Drakeford made a short address before the Wales Herald of Arms Extraordinary, Tom Lloyd, made the Proclamation in English and the Lord-Lieutenant of South Glamorgan, Morfudd Meredith, proclaimed King Charles in Welsh.
After the readings, members of 104th Regiment of the Royal Artillery fired a 21-gun salute before the singing of God Save The King and Hen Wlad Fy Nhadau, Wales’s national anthem.
It was the third time in three days that artillery fire has resounded across the Welsh capital to mark both the Queen’s death and the accession of her son to the throne.
When the gun salute ended, soldiers were ordered to remove their head dresses while a call was made for “Three cheers for His Majesty the King”.
Welsh Secretary Robert Buckland attended the ceremony alongside Wales’ opposition leaders.
Other dignitaries included South Glamorgan High Sheriff Rosie Moriarty-Simmonds.
Flags on the castle and council buildings which had been returned to full-mast on Saturday to coincide with the Reading of the Principal Proclamation of the new monarch in London were lowered to half-mast again following the event.
The Senedd was recalled at 3pm to allow members to pay tribute to the Queen.
All other business has been suspended until after the state funeral on Monday September 19.