Prince William and Kate Middleton have paid tribute to Prince Philip with a picture of the smiling Duke on their website.
The couple's official Royal Foundation site now shows a black-and-white image of the Prince, who died on Friday aged 99.
William had been due to appear at last night's Bafta awards, but withdrew following his grandfather's death.
He is due to walk behind the Duke's coffin alongside his brother Harry at next week's funeral - amid hopes the pair can heal their rift.
A statement shared by William and Kate after Prince Philip's death said: "It is with deep sorrow that Her Majesty The Queen has announced the death of her beloved husband, His Royal Highness The Prince Philip, Duke of Edinburgh.
"His Royal Highness passed away peacefully this morning at Windsor Castle.
"The Royal Family join with people around the world in mourning his loss.
"Further announcements will be made in due course. Visit www.royal.uk to find out more."
A memorial service is being held at Canterbury Cathedral today as part of eight days of mourning ahead of next Saturday's funeral.
This morning former Prime Minister Sir John Major spoke of the support given to the Queen by the Duke of Edinburgh.
He told the BBC's Andrew Marr Show: "Consider the position the Queen is in. She is the head of state, that is a very lonely position in many ways.
"There are a limited number of people to whom she can really open her heart, to whom she can really speak with total frankness, to whom she can say things that would be reported by other people and thought to be indelicate. Of the handful of people to whom she can speak frankly, her husband, Prince Philip, was obviously the first one.
"At times of difficulty, he was the person who was there, he was the person to whom she could unburden herself.
"And when you're facing a sea of problems, as she so often was, and sometimes when you're overwhelmed by what has to be done, someone who understands that, someone that can take part of the burden, someone who can share the decision-making, someone who can metaphorically - or in the case of Prince Philip, I think, probably literally - put their arms around you and say 'it's not as bad as you think, this is what we have to do, this is how we can do it, this is what I think' - I think when you talk of him being a great support, that was it."
