Having a faulty BRCA gene - either BRCA1 or BRCA2 - is known to increase a woman's risk of both cancers, although the exact percentage of risk increase is still unclear.
Currently, women are eligible for testing for the faulty genes if they have a close family history of cancer, usually meaning a parent or sibling has been affected.
But researchers from Barts Cancer Institute at Queen Mary University of London said screening all women could cut cancer cases in the UK.
Some women found to have a faulty BRCA gene, such as Angelina Jolie, choose to have preventative surgery, such as a double mastectomy, to limit their chances of a breast cancer diagnosis in the future.
In addition, women with a faulty BRCA gene and a family history of ovarian cancer sometimes opt to have their ovaries removed as a preventative measure.
The research suggests testing all women over 30 could result in up to 17,000 fewer ovarian cancers and 64,000 fewer breast cancers over a lifetime.
Previous studies have shown women carrying either a BRCA 1 or BRCA2 gene mutation have between a 17-44% chance of developing ovarian cancer and a 69-72% chance of developing breast cancer over their lifetime.
Among women who don't carry the gene mutations, the risk of ovarian cancer is 2% while the risk of breast cancer is around 12.5%.
The researchers used mathematical models to compare costs and health benefits of different strategies for genetic testing.
They concluded that testing all women over 30 could not only reduce cancer cases and save lives, but also save money through the reduced need for cancer treatment.
Commenting on the findings, Dr Rosa Legood from the London School of Hygiene and Tropical Medicine said: "Our analysis shows that population testing for breast and ovarian cancer gene mutations is the most cost-effective strategy which can prevent these cancers in high risk women and save lives.
"This approach can have important implications given the effective options that are available for ovarian and breast cancer risk management and prevention for women at increased risk."
Athena Lamnisos, CEO of The Eve Appeal, which funded the research, added: "These research findings demonstrate the potential for both saving lives and costs. Whole-population genetic testing is cost-effective.
"If women identified as high risk act on the information that they're given, in terms risk reducing surgery, their lifetime risk of developing these women-specific cancers can be reduced. The impact that this study could have on healthcare in the future for these cancers is promising and an exciting step forward in prevention."
Professor Diana Eccles, Cancer Research UK's expert on cancer genetics, agreed the study "provides useful insight into the potential cost-effectiveness of genetic testing" but warned we must "tread with caution".
"We are probably some distance from safely implementing population genetic testing for cancer risk because there are still too many untested assumptions," she said.
"For example. risk estimates are still not very precise for most of the genes suggested for inclusion in this scenario. And for some women, finding out they carry a mutation could cause unnecessary anxiety.
"We need to improve our understanding of what to do with this genetic information and work with the public to ensure there is a better understanding of the pros and cons of genetic testing."
Genetic testing explained:
If a close family member (defined as a parent, child or sibling) has been diagnosed with cancer or been found to have a faulty gene, visit your GP to see if you're eligible for genetic testing.
According to Cancer Research UK, your GP will refer you for a genetic assessment for BCRA genes if you have any of the following:
one first degree female relative diagnosed with breast cancer aged younger than 40 (a first degree relative is a parent, sibling or child)
one first degree male relative diagnosed with breast cancer at any age
one first degree relative with cancer in both breasts where the first cancer was diagnosed aged younger than 50
two first degree relatives, or one first degree and one second degree relative, diagnosed with breast cancer at any age (second degree relatives are aunts, uncles, nephews, nieces, grandparents, and grandchildren)
one first degree or second degree relative diagnosed with breast cancer at any age as well as one first degree or second degree relative diagnosed with ovarian cancer at any age (one of these should be a first degree relative)
three first degree or second degree relatives diagnosed with breast cancer at any age