Prince Philip death: The Duke of Edinburgh dies, aged 99
Prince Philip died at Windsor Castle on 9 April, Buckingham Palace confirmed on Friday.
Harry and Meghan updated their website, Archewell.com, on Friday afternoon, to share a message reading "In loving memory of the Duke of Edinburgh" and the dates 1921-2021.
The website also said: "Thank you for your service...You will be greatly missed."
Harry and Meghan have been living in Canada and the US since November 2019, but were keeping in touch with his grandfather via video calls in recent months.
Earlier this year, the Duke and Duchess of Sussex sat down for an interview with US chat show host Oprah Winfrey in which they laid bare their grievances with the royal household.
The interview aired in the US and the UK when the Duke of Edinburgh was still in hospital in what became his longest stay at four weeks, during February and March.
The couple faced criticism for the date the show aired, but they did not have any control over the decision.
While they did make some significant claims about their time as senior royals, including an allegation of racism, they exonerated the Queen and Prince Philip from those allegations.
In a previous interview with James Corden, Harry had revealed he had been keeping up with the Queen and Philip via video calls, and that the great-grandfather had been able to watch Archie playing in their new Californian home.
But he died before he was able to meet his 11th great-grandchild, as the Duchess of Sussex has not yet given birth to her second child.
Asked about whether the Queen can use Zoom, Harry said: "Both my grandparents do, we have Zoomed them a few times.
"They've seen Archie running around.
"But my grandfather instead of pressing leave meeting, he just goes 'doof'," he said miming closing a laptop.
Watch: Prince Harry reveals Archie's first word and what the Queen got him for Christmas
During the Winfrey interview, Meghan indicated she was still close to the Queen despite the huge physical distance, saying she had "picked up the phone" and called her when she heard the news in February that Philip had gone into hospital.
It's not yet clear if the couple will be able to travel to the UK for a funeral. Harry is said to be "likely" to come back.
Meghan is due to give birth in the summer, and as they currently live in the US, they are subject to restrictions for travel.
Flying when pregnant can be safe, but tends to be advised against after the 37th week according to the NHS.
Some airlines will require doctors' notes if the woman is 28 weeks pregnant or more.
All travel corridors were suspended by the UK in February, meaning those arriving in the country need to quarantine for 10 days.
However as the US is not on the red list, quarantine does not need to be done in a government approved hotel.
Harry and Meghan would have to present negative coronavirus tests during their quarantine according to the government regulations.
There are exceptions given on compassionate grounds, for which a funeral would qualify.
Watch: First Minister Offers Sympathies to UK's Queen Elizabeth On Death of Prince Philip