The pensioner, who presented the watch on the American version of the programme, revealed that he had paid just $ 120 (£97) and had saved for it with his salary from the army, which was just under $ 100 a month.
He explained that he bought it over 50 years ago and Peter Planes, who was valuing the timepiece, could not hide his excitement when he laid eyes on it.
He told the veteran: “I was very excited when you brought this up to the table. It is the first model GMT that Rolex ever made.”
Peter went on to add: “I’m very pleased to tell you that this watch is a very, very collectible watch.”
The pensioner was then left speechless when he was told how much the timepiece was worth and let out a huge breath as he took in the information.
Peter revealed that on its own the watch would cost between $ 35,000 (£28,542) and $ 45,000 (£36,700).
But, he added that because the elderly gentleman had saved the box that it was presented in and paper work, it was worth a lot more.
Peter noted: “This watch is worth much more because you saved the box. Easily today it is worth $ 65,000-$ 75,000.”
The man simply said, “Wow,” as he digested the information and appeared close to tears as Peter joked that it was certainly worth more than one month’s salary in the army now.
As he regained his composure, the pensioner explained: “I had no idea. I’m speechless. If you would have told me $ 1,500 I would have been happy.”
The shock valuation, which took place in April 2016, has racked up more than 1.9 million views on YouTube with viewers left stunned by the final estimation.