Jim Pedgrift was visiting the Capital when he slipped on a cobblestone path, rupturing the tendon to his left quadricep.
The 74-year-old, from Santa Rosa, California, was rescued by a middle-aged couple who lifted him to safety on Princes Street, while a doctor who was passing by quickly summoned an ambulance.
Staff at the Edinburgh Royal Infirmary told Mr Pedgrift, a semi-retired maths lecturer, that he would need reconstructive surgery to repair the injury – but he decided to wait until he got home to have the operation.
Now, a week after his surgery, Mr Pedgrift faces six weeks in braces before physical therapy, but wants to track down and thank the mystery heroes.
He said: “I am left with a persistent and somewhat nagging feeling that there is a debt that can never be repaid but needs to be acknowledged.
“I will always be grateful to the citizens of Edinburgh who came to my aid and extended gratuitous kindness to a stranger.”
Mr Pedgrift, who wrote to the Evening News shortly after his operation, had been enjoying a holiday in the Capital with his wife and three friends.
They came to Scotland to complete the 140-mile Rob Roy Way from Drymen to Pitlochry but, before returning to the US, paid a flying visit to Edinburgh.
The accident happened on July 4, after the group had taken a bus tour of the city.
Mr Pedgrift decided to explore the sculptures in Princes Street Gardens while the rest of his group went shopping on Princes Street.
He said: “The tour guide said there was a sculpture in the park of a bear [Wojtek] and a soldier which seemed more interesting to me than shopping. I walked up Princes Street looking for a way down into the park and then I came upon a narrow cobblestone path down. It was raining lightly but there was a handrail so I decided to give it a go. The fall occurred halfway down the path.
“It happened so fast all I remember is I knew immediately I was in trouble. Unknown to me I had just torn my left quadricep tendon from my patella, but what I was fully aware of was the excruciating pain and the fact I was unable to move my left leg.”
He added: “Many people helped me in my moment of need and I wish I could thank them all personally.
“One person stands out in my memory – the first gentleman who came up the path and picked me up in the rain. Once on my feet he could have left me, but he didn’t. He put his umbrella over my head and let the rain fall on his own. He carried me, a stranger, back up the path to the street.
“Once seated on a bench he could have left me but he didn’t. Simple acts of kindness are like little mini-miracles, they defy analysis and explanation.”