The discovery could also lead to the development of preventative treatments for people who are at risk of developing CLL.
Dr Chris Pepper, a senior lecturer in haematology at Cardiff University, led the research, reports Madeleine Brindley of Western Mail.
He said: "For years we have known that there is a familial link to this disease and we have thought that there must be a genetic link, but this is the first study to show that there is one.
"For years the Holy Grail of cancer research has been to find a particular gene that gives you cancer.
"In CLL there is no single gene that causes it. But the reason why this study is so important is that it shows that very subtle changes in the genetic profile can lead to a higher risk.
"It doesn't mean that people who have these genetic changes will get CLL, but it does mean they have a higher risk."
CLL is cancer of the white blood cells called lymphocytes, which fight infections, and is the most common form of chronic leukaemia.
It is estimated that there are 4,000 new cases diagnosed every year in England and Wales - some 5% of these patients will have a relative who has had the disease.
The Cardiff University and Sutton-based Institute of Cancer Research study found the six genes after comparing the genetic make up of patients with CLL to those without the disease.
Dr Pepper said the genetic variations found occurred naturally and are different to genetic mutations common to other forms of cancer, which can cause the disease.
"These are naturally occurring variations in genetic material than can subtly alter the expression of a gene," he said.
"If a person has one of these variations it gives a slightly elevated risk of CLL; if they have two, three or four, the chances of getting CLL increase with every incidence."
He added: "This research provides strong evidence that CLL, in at least some cases, is caused by a combination of different genetic variations which are inherited.
"Each of these variations by itself has a very small effect on the risk of developing this leukaemia, but when all of them are present there is a significantly increased risk of leukaemia."
Dr David Grant, scientific consultant at Leukaemia Research, said: "This finding is very exciting as it carries the possibility of improving treatments for individuals who we know are at risk of developing this leukaemia.
"Clinical applications are still a little while away but this is a very important step forward in understanding the basis of this common leukaemia."