"He is continuing to make good progress and is in very good spirits," said a royal source. "He is doing this engagement because it is something he has been committed to for a very long time, as well as it being something he takes extremely seriously."
Buckingham Palace have said that the 92-year-old Duke, who is Britain's longest serving royal consort, will present medals to Professor Sir John Cadogan, the former head of research at BP, Professor Mike Ferguson, dean of Research in Life Sciences at Dundee University, and Sir Ian Wood, who is the former chairman of the oil and gas services company Wood Group, who are based in Aberdeen.
The Royal Society of Edinburgh is one of Prince Philip's oldest patronages and he has presented the royal medals there several times in the past.
After his engagement on Monday the Duke will travel to Balmoral where he will be reunited with the Queen, who is currently on holiday there.
Queen Elizabeth II travelled alone to her summer retreat in the Scottish Highlands on 26 July and it was hoped that her husband would soon be able to join her.
While he is at Balmoral, Philip is expected to meet his third great-grandchild Prince George of Cambridge for the first time, when Prince William and Kate Middleton visit the royal family.
Prince Philip, who has been recuperating at Windsor Castle and Sandringham since undergoing abdominal surgery on 6 June, is expected to stay at Balmoral until October, when he will return to London.
As a result of his surgery the Duke of Edinburgh was forced to miss the Queen's official birthday celebrations at Trooping the Colour, Royal Ascot and the Garter Service at Windsor, but the royal family were quick to rally around him with many of them visiting him while he was in hospital and at the royal residences.