The Scottish world number four tennis star was presented with his honour at Buckingham Palace yesterday, months after becoming the first male British tennis player in 77 years to win the men's singles title at SW19.
Murray told the future King - who was taking part in his first investiture ceremony as he steps up to support The Queen - that his wife Kate's handwriting was better after receiving a letter of congratulations for his achievement.
Clutching his accolade for services to tennis, Murray said: "After Wimbledon his wife had written a letter to say congratulations and she had amazing handwriting, and I had a letter from Prince William before and his handwriting was not good. And I just said, 'could you pass it on that her handwriting was fantastic and thank you very much for the letter'."
The Dunblane-born star said receiving the honour had been a "special day".
Punctual Murray arrived well ahead of the investiture with girlfriend Kim Sears and his parents Willie and Judy, but before he appeared he tweeted about being held up by a drugs test.
The Duke appeared to give a faultless performance as he presided over the ceremony, presenting awards, dubbing new knights and recognising the efforts of senior members of the Armed Forces.
After the event in the palace's lavish ballroom, Murray said: "It's a great honour to be awarded something like this - it means a lot.
"Speaking to some of the people and the stuff they've done it's pretty incredible, it was nice to come along and receive it today.
"I've wanted to do it sooner but because of all the travel and stuff I've always been away on the dates that we've been given."
The lack of a homegrown winner of the Wimbledon men's title had hung over British tennis for decades, but Murray beat all comers and triumphed in the final - against Novak Djokovic - to become the first British man since Fred Perry to win the singles title at Wimbledon.
He added: "He just asked me about what it's been like after Wimbledon. I think he's a big sports fan, he was at the Olympics, he was seen everywhere and I've seen him a couple of times at Wimbledon, so today was nice and it was his first time as well, so a special, special day."
The British number one player is recovering from back surgery and said he had a rehab session planned for the afternoon but would probably stop off somewhere on the way home for a celebratory lunch.