The Royal Family have led the well-wishers, with a message on the monarchy's official Twitter account wishing him a "very happy birthday" alongside a picture on the balcony of Buckingham Palace.
According to Sky News, Kensington Palace thanked those who had sent messages to the duke, tweeting: "Thank you for all the birthday wishes and kind messages." The duke will be celebrating the final birthday of his 30s after surprising runners at a race around Sandringham Estate on Father's Day.
Prince William was pictured at a microphone with his two eldest children, Prince George and Princess Charlotte, counting down to the start of the race. Brian Cook, who participated in the run and photographed the royal trio, sharing the snap on Twitter, said it was a "nice surprise, and nice of them to do".
Run Sandringham was welcoming hundreds of runners of all abilities and ages to run a half-marathon, a 5K or a community mile, with the aim of raising "many thousands of pounds for good causes".
It is understood that the Duke of Cambridge was not running in the event and was there in a private capacity.
He was seen wearing a blue shirt and a pair of navy chinos, while George and Charlotte were photographed wearing shorts and trainers.
Another Run Sandringham event is due to take place on September 26, when it's hoped there will be no social distancing restrictions needed.
The event boasts a scenic route around the grounds of Sandringham Estate, the Queen's winter retreat.
Prince William, who is second in line to the throne after his father, Prince Charles, was born at St Mary's Hospital in Paddington at 9.03pm on 21 June 1982.
He was Charles and Diana's first-born son and weighed 7lb 1.5oz.
He accompanied his parents on a six-week official visit to Australia and New Zealand, aged only nine months, which was a break from royal tradition.
William's mother, who separated from Charles in 1992, died in a car crash in 1997. He was just 15 and his younger brother Harry was 12, and the brothers walked behind the princess's coffin during a funeral procession through London.
William met Kate Middleton at St Andrews University in Fife, Scotland, and the pair wed in 2011 after dating for more than eight years. He was made the Duke of Cambridge by his grandmother, the Queen, on the morning of his wedding.
The couple welcomed their first child, George - also a future king - in 2013. George was followed by Charlotte in 2015 and Louis in 2018.