Two pills a day for two years reduced the incidence of bowel cancer by 63% in a group of 861 at-risk patients, a study reported in The Lancet said.
Newcastle University's Prof Sir John Burn, who led the study, said the evidence "seems overwhelmingly strong".
Other experts said the findings added to a growing body of proof that aspirin could be used in the fight with cancer.
The study was conducted on 861 patients with Lynch syndrome, which affects one in every 1,000 people.
They struggle to detect and repair damaged DNA which means they are more likely to develop a range of cancers including those of the bowel, womb and stomach.'Good deal'
When looking at all patients in the trial, those in the group given 600 milligrams of aspirin every day developed 19 tumours compared to 34 tumours in the other "control" group, a reduction of 44%.
When the researchers looked at just those patients who took the medication for at least two years the reduction was 63%.
There was also an effect on other cancers linked to Lynch syndrome, which fell by half in the treatment group.
Prof Sir John Burn, from Newcastle University, said there were 30,000 adults in the UK with Lynch syndrome.
If all were given the treatment he said it would prevent 10,000 cancers over 30 years and he speculated that this could possibly prevent 1,000 deaths from the disease.
However, there would also be side effects.
"If we can prevent 10,000 cancers in return for 1,000 ulcers and 100 strokes, in most people's minds that's a good deal," he said.
"People who've got a clear family history of, particularly, bowel cancer should seriously consider adding low dose aspirin to their routine and particularly those people who've got a genetic predisposition."
Aspirin is already well known to reduce the risk of heart attack and stroke in high risk patients.Continue reading the main story
Audrey Francis describes herself as "a bit of a walking time bomb".
There is a history of cancer in her family and she has been diagnosed with Lynch syndrome.
Seventeen years ago she had a hysterectomy. That was when doctors discovered she had not one but two cancers - in the womb and the ovaries.
Tests showed she had a chunk of DNA missing which was causing the cancers: "I actually had the inability to stop the cancers developing," she said.
She took part in the trial and has since decided to self medicate with aspirin: "I've got my fingers crossed and I'm hoping it'll do the trick for me."Other studies over the past two decades have suggested the pain killer reduced cancer risk, but this was the first randomised control trial, specifically for aspirin in cancer, to prove it.
In 2010, a study suggested patients given aspirin had a 25% lower risk of death during that trial.
Prof Peter Rothwell, from Oxford University, who conducted that study said the latest research "certainly helps to build a consistent picture, all pointing in the same direction that there is a link with cancer".
Cancer Research UK's Prof Chris Paraskeva said: "This adds to the growing body of evidence showing the importance of aspirin, and aspirin-like drugs, in the fight against cancer."'Balanced argument'
One of the questions asked by the research into aspirin was whether healthy people with no family risks should take the drug.
The lower the risk of heart attack or cancer, the lower the benefit of taking aspirin, yet there are still potentially deadly side effects.
Sir John said that it was a "finely balanced argument" and that he decided the risks were worth it for him.
"I think where we're headed for is people that are in their 50s and 60s would look very seriously at adding a low dose aspirin to their daily routine because it's giving protection against cancer, heart attack and stroke.
"But if they do that they've got to have their eyes wide open. They will increase their risk of ulcers and gastrointestinal bleeds and very rarely they will have a stroke caused by the aspirin."