A third commented: "Happy birthday and best wishes to His Royal Highness the Duke of Edinburgh!".
Prince Andrew and Princess Eugenie also celebrated Philip's special day on social media.
The Duke and Duchess of Cambridge wished Philip many happy returns by sharing some lovely photos on Twitter and Instagram with the caption: "Wishing a very Happy 98th Birthday to His Royal Highness The Duke of Edinburgh!".
Philip, who has been married to the Queen for more than 71 years, is edging closer to his milestone 100th birthday in 2021.
In the second snap, a black and white photo from the family archive, Prince Philip can be seen dancing with a young Queen Elizabeth.
The Royal Family's official Instagram account also shared a birthday message, posting photos of the senior royal at Lady Gabriella Windsor and Thomas Kingston's wedding this year and photographed in 1953 - 66 years ago. "The Duke of Edinburgh was born on this day in 1921".
While the Queen had a busy set of engagements last week, entertaining US President Donald Trump and his wife Melania, commemorating the 75th anniversary of D-Day, and attending the Trooping the Colour celebrations, Philip will have been enjoying his time away from the limelight.
After being educated in France, Germany and the United Kingdom, he joined the British Royal Navy in 1939, aged 18.
He left active military service in 1952 when Elizabeth ascended the throne and was by her side, supporting her with her royal duties until his retirement.
Aside from a hip replacement in 2018, he is said to be in good health. The Duke and Duchess of Cambridge shared individual shots of themselves laughing with Philip, a pic Philip and the Queen and a photo from the 2016 Trooping of the Colour event.
Got a story tip or just want to get in touch?