There were only 30 people inside the chapel, including Queen Elizabeth II, her four children and her eight grandchildren, because of coronavirus restrictions.
The service, which celebrated his naval past, his international heritage and seven decades of service, commenced after a national minute’s silence was held at 3pm local time.
On and off-air, British celebrities paid tribute to the duke, who had been married to the queen for 73 years.
Both the BBC and ITV covered the historic ceremony, allowing the British public to watch it from their homes.
During the BBC broadcast, noted presenter and natural historian Sir David Attenborough led the celebrity tributes, as he shared memories of working with the royal, praising him for getting involved with conservation efforts even when it "didn't mean much to many people".
"The World Wildlife Fund owed a huge amount to his presence," he said during the coverage. "When he spoke about conservation, he spoke about it with passion and knowledge."
Of the duke's character, Attenborough added: "He was an extraordinary combination of being formidable and friendly. You knew he was there. He had an amazing presence. It was an extraordinary balancing act between formality and informality."
Online, Australian singer-songwriter Kylie Minogue led the tributes. She shared a photograph of herself with Prince Philip on Twitter, writing in the caption: "RIP HRH Prince Philip. What an honour it was to meet at Windsor Castle."
One Direction singer Liam Payne, meanwhile, honoured the duke with a watercolour portrait. On Instagram, he wrote, alongside an image of the painting: "Rest in peace HRH Prince Philip, finished this off whilst listening to your life, what a great legacy left behind."
Former Good Morning Britain host Piers Morgan commented on the images of Queen Elizabeth II sitting alone at the ceremony owing to social distancing measures.
"Has there ever been a more heart-breaking picture of the Queen?" Morgan wrote on Twitter. "The cruel separation and loneliness suffered by so many in this pandemic, now endured by the world’s most famous woman as she says goodbye to her husband of 73 years. Just devastating."
Morgan had previously taken to Twitter on the day of Prince Philip's death to pay tribute to a "truly great Briton who dedicated his life to selfless public duty and was an absolute rock of devoted support to Her Majesty, The Queen".
"A very sad day for our country," he added. "Thank you, Sir."
English television and radio presenter Fearne Cotton also shared a photo of the queen sitting alone.
"The shots on the BBC of Her Majesty the Queen alone are breaking my heart in two," Cotton wrote on Instagram. "A beautiful ceremony. A long, amazing life celebrated so perfectly."
Morgan's former colleague and Good Morning Britain presenter Kate Garraway, whose husband recently returned home after more than a year in hospital being treated for Covid-19, also shared a touching image of the queen.
"So alone – my heart breaks for her and so, so many others who have lost loved ones this year," she wrote. "Just shows whoever you are the pain of grief and the loneliness it brings."
Dame Darcey Bussell, a retired ballerina and former judge on BBC's Strictly Come Dancing, told her Instagram followers that she would be backing the effort to get one million more young people doing their Duke of Edinburgh's Award, "to show the potential today's youth have".
"#DofELivingLegacy will help @DofEUK give one million more young people, from all circumstances and backgrounds, the opportunity to do their DofE over the next five years."
She left a link where people can donate to the Living Legacy Fund, a new fund that has been set up in the duke's memory.
Broadcaster Ruth Langsford also paid her respects to the queen, writing on Instagram: "My heart is breaking for her. RIP Prince Philip."
Singer and TV star Peter Andre added two posts to his Instagram feed, paying tribute to the duke and leaving a message for the queen, next to an image of her sat alone in the pews. "No matter how strong she has been her whole life. Truly heartbreaking."