On several occasions the comedian left the VIP area to take part in the gruelling hill race, and even wore full Highland dress to watch the games afterwards.
Connolly said last night: "Robin was both my friend and my hero, a unique talent and a kind and generous man; the world will be a much poorer place without him."
Connolly's wife, Pamela Stephenson Connolly, added: "Robin was one of the most uniquely brilliant and complicated comic artists the world has ever known.
"As a performer, he navigated a dangerous high wire at every single moment - with no safety net. My husband and I loved and admired him deeply and will miss him in a way that is beyond words."
Tributes were also paid by former secretary of the games, George Thomson, who said Williams always had time for anyone who wanted to talk to him or pose for a picture.
Mr Thomson said: "He would light the place up. The whole place seemed to stand up when he appeared.
"He always took everyone on - no matter who it was, he would give them his time."
Another Scot who encountered the actor during his holiday was renowned Nessie hunter Steve Feltham, who told how Williams and Connolly shared a cruise on Loch Ness in 2001.
"He was a lovely man. Very approachable and down to earth", said 51-year-old Mr Feltham.
"I remember thinking that of all the people on board, Robin Williams was the most approachable and nicest person . He was quality. We talked a lot about the Highlands and he was very knowledgeable. He knew all about the way of life, the Highlanders, the Gaelic language and the Clearances.
"He knew about Loch Ness and Nessie and was keen to learn more."