President Tony Tan Keng Yam has written to Queen Elizabeth of the United Kingdom, and the Duke and Duchess of Cambridge - Prince William and his wife Catherine - to convey his best wishes on the birth on Monday of the Prince of Cambridge.

Prime Minister Lee Hsien Loong has also written to the Duke and Duchess to convey his congratulations.

"We were delighted to hear news of Her Royal Highness the Duchess of Cambridge's pregnancy shortly after Their Royal Highnesses' visit to Singapore in September 2012, as part of their tour of the Commonwealth to commemorate Your Majesty's Diamond Jubilee celebrations," Dr Tan said in his letter to Queen Elizabeth.

"I have no doubt that your great-grandson will be blessed with good fortune," Dr Tan said, adding that he and his wife share in the joy and the celebration of the British people.

In his letter to Prince William and his wife Catherine, Dr Tan said, "My wife, Mary and I send you our warmest congratulations on the birth of your first son."

"The people of Singapore recall Your Royal Highnesses fondly," Dr Tan said, according to a statement from Singapore's Foreign Affairs Ministry on Tuesday.

Prime Minister Lee, in his letter to the Duke and Duchess of Cambridge, said, "We remember warmly your visit to Singapore last year, and are delighted at the happy news."

"I wish Your Royal Highnesses and the Prince of Cambridge happiness and good health always," Mr Lee added.