Finding tumours when they could still be surgically removed would be "a night and day difference" for survival, said Dr Tomasetti.
CancerSEEK is now being trialled in people who have not been diagnosed with cancer, which will be the real test of its usefulness.
The hope is it can complement other screening tools such as mammograms for breast cancer and colonoscopies for colorectal cancer.
Dr Tomasetti said: "We envision a blood test we could use once a year."
The CancerSEEK test, reported in the journal Science, is novel because it hunts for both the mutated DNA and the proteins.
Increasing the number of mutations and proteins being analysed would allow it to test for a wider range of cancers.
Dr Gert Attard, team leader in the Centre for Evolution and Cancer at the Institute of Cancer Research, London, and consultant medical oncologist at the Royal Marsden NHS Foundation Trust, told the BBC: "This is of massive potential.
"I'm enormously excited. This is the Holy Grail - a blood test to diagnose cancer without all the other procedures like scans or colonoscopy."
He said "we're very close" to using blood tests to screen for cancer as "we have the technology".
But he cautioned there was still uncertainty about what to do when a cancer was diagnosed.
In some cases, the treatment may be worse than living with a cancer that is not immediately life-threatening.
Men can already have slow growing prostate cancers closely monitored rather than treated.
"When we detect cancer in a different way, we can't take for granted that everyone will need treatment," Dr Attard said.
Early stage cancers
Prof Richard Marais, from Cancer Research UK, said it would take time to prove that it worked as an early diagnosis for cancer - at least five to six years.
"Detecting cancer early, before the disease has spread is one of the most powerful ways to improve cancer survival and this interesting research is a step towards being able to do this earlier than is currently possible."
Paul Pharoah, professor of cancer epidemiology at the University of Cambridge, said more work was needed to assess how the test performs when cancers are less advanced.
He said: "Demonstrating that a test can detect advanced cancers does not mean that the test will be useful in detecting early stage symptomatic cancer, much less pre-symptomatic cancer. The sensitivity for the stage 1 cancers in the study was only 40%."
And Dr Mangesh Thorat from the Centre for Cancer Prevention, Queen Mary University of London, said it looked promising "but with several caveats"
"A significant amount of further research is needed before we can even contemplate how this might play out in screening settings," he said.
"This is only a case-control study, and therefore needs further evaluation in large cohorts more representative of general population where such screening might be introduced."
The cost of CancerSEEK is less than $500 (£360) per patient, which is around the same price as a colonoscopy.