The video was recorded at Clarence House and shows the duchess speaking directly to camera.
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Clarence House has been her London home since 1953 and has been witness to many of her birthdays.
In a recording from Clarence House, the prince said he remains concerned about climate change and possible long-term environmental damage.
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Prince William departed from Clarence House in a chauffeured, plum-colored Bentley, accompanied by his younger brother and best man, Prince Harry.
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The previous record, of 59 years, two months and 13 days, was set by his great-great-grandfather, King Edward VII, Clarence House said.
Two days of the trip will be spent privately, said Clarence House.
Later the prince and the Duchess of Cornwall toured a Waitrose store in Belgravia, close to their Clarence House home in central London.
He recently held a reception at Clarence House to congratulate 14 hospitals which have signed up to standards like eliminating hydrogenated fats from their food.
The princes would be prepared to meet the ex-royal servant, said Clarence House although there are said to be no immediate plans for a meeting.
Clarence House said those illnesses were not related to her current condition, but that the Duchess would have to cancel some planned engagements during her recovery.
The duchess is not yet 12 weeks pregnant, Clarence House told CNN on Monday, so the palace is not announcing a due date for the child.
William, who recently gained a 2:1 in his geography degree at St Andrews University, was invited to support the British and Irish Lions by coach Sir Clive Woodward, Clarence House said.
He recently moved out of his father's residence, Clarence House -- where he had a bedroom and study -- into a small flat at Kensington Palace where his brother and sister-in-law live.
The couple visited Westminster Abbey, where the president laid a wreath at the Grave of the Unknown Warrior, and went to see the Prince of Wales and the Duchess of Cornwall at Clarence House.
The wife of a British King is automatically his Queen Consort - as, incidentally, Prince Charles is only too well aware, despite Clarence House's attempts to suggest that Camilla will merely be "Princess Consort".
Prince William and Kate Middleton are engaged to be married in London in the spring or summer of next year, Clarence House has announced, ending months of speculation about when the young couple would finally tie the knot.
The paper comes in a wrap-around cover which shows the couple driving from Buckingham Palace to Clarence House in Prince Charles' Aston Martin, describing it as "one of many such small moments that revealed a new brand of royalty".
Although most of the furniture was bought by Braka and Graham, the couple enlisted Robert Kime, the celebrated decorator who was appointed by the Prince of Wales to renovate Clarence House, to design the bedrooms and sitting rooms in his trademark style of fine upholstery mixed with English and Ottoman fabrics.
Ridge -- a former Marine, decorated Vietnam veteran, former congressman and two-term governor of Pennsylvania -- took the oath of office from Supreme Court Justice Clarence Thomas at the White House.
The defendant Mr Clarence is also charged with aggravated vehicle taking causing the death of Constable Reynolds, the burglary of a house in Fountain Hill and assisting an offender with intent to impede his apprehension or prosecution by changing clothing in an apparent attempt to disguise identity.
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