Doctors cannot be certain it was the treatment that led to the miraculous outcome, but know of no other explanation.
Results from an early-stage trial of the drug indicate that it may offer a potential "paradigm shift" in cancer therapy, according to the patient's consultant.
The drug, pembrolizumab, is the latest in a new generation of treatments that prevent cancers shielding themselves from the immune system.
Story continues below the slideshow:
It was tested on melanoma - the most dangerous form of skin cancer - because the prospects for patients with advanced forms of this disease are so bleak.
Just under 70% of the 411 patients taking part in the trial were still alive one year after starting on the treatment.
The result is considered remarkable because all had highly advanced melanoma and a very poor prognosis.
Currently one-year survival rates for untreated patients diagnosed with advanced Stage Four melanoma are just 10% for men and 35% for women.
The "cured" trial patient, a man from London, has undergone six months of treatment with pembrolizumab, which is injected into the bloodstream.
Doctors were astonished when after just three months his tumours had almost disappeared. Since then they have shown no sign of returning - and in fact have shrunk even further.
His consultant Dr David Chao, from the Royal Free Hampstead NHS Trust in London, said: "We cannot say for certain that he's been cured, but he is doing very well. He was aware that without an effective treatment his survival prospects were not good - maybe months.
"Pembrolizumab looks like it has potential to be a paradigm shift for cancer therapy and is firmly helping to establish immunotherapy as one of the most exciting and promising treatment modalities in recent years.
"This is one of several new drugs of this type being produced. What these early trials are showing is that they are fulfilling their promise ridiculously fast.
"Some of these results are really astonishing; almost jaw-dropping. And these drugs may be applicable to many different cancer types, including ones that are hard-to-treat such as lung cancer.
"Cancers adapt to treatments, and when they come back they are harder to treat. Can we dream about actually curing some of our patients with very advanced cancer? Once we get the immune system attacking the cancer, can it act independently to keep the cancer under control? We don't have all the answers yet, but that's what we're looking at."
Pembrolizumab is a synthetic antibody that blocks a biological pathway called programmed cell death 1 (PD-1) which cancers activate to suppress the immune system.
In healthy individuals, PD-1 is part of the process that applies a "brake" to the immune system and prevents it from running out of control.
Without the brake, there is a risk of a harmful inflammatory reaction - a potential serious side effect of the new drugs.
Pembrolizumab was generally "well tolerated" by the trial patients, according to Dr Chao. However, he said responses varied widely between different individuals.
Results from the trial were presented at the annual meeting of the American Society of Clinical Oncology in Chicago.
Clinicians do not yet know the true extent of how pembrolizumab might affect survival. After 18 months, 62% of patients were still alive and undergoing treatment.
In addition, around 80% of patients responded to the drug - an unusually high proportion.
A total of 72% experienced tumour shrinkage, including 39% whose tumours were more than halved in size according to one kind of assessment.
Additional data showed that the drug also reduced the size of advanced non-small cell lung cancers by up to 47%.
Pembrolizumab's manufacturer, the pharmaceutical company Merck Sharp & Dohme, is expected to apply for a European licence to market the drug within months.
Each year, around 13,300 people in the UK are diagnosed with melanoma - more than a third of them aged under 55.
Gillian Nuttall, founder of the charity Melanoma UK, said: "Advanced melanoma is a terrible disease with a poor prognosis. Pembrolizumab represents the latest advance in a whole raft of new treatments in advanced melanoma which have come through over the past few years.
"The pembrolizumab results are really exciting and could represent a turning point for patients affected by advanced melanoma giving them a greater chance of survival."