Researchers from the University of Southampton and University Hospital Southampton Foundation Trust examined the cases of 2,850 women under the age of 41 who were diagnosed with breast cancer and treated in the UK.
The Prospective Outcomes in Sporadic versus Hereditary breast cancer (POSH) study found that there were no significant differences in cancer recurrence rates after treatment for women with a history of breast cancer in their family compared with those without.
Ramsey Cutress, an associate professor in breast surgery, said: "Successful treatment for breast cancer is just as likely in young patients with a family history of breast cancer, as in those without a family history.
"Patients with a family history of breast cancer can therefore be reassured that their family history alone does not mean that their outcome will be worse."
The researchers now plan to investigate whether certain breast cancer gene variants have any impact on the effectiveness of different anti-cancer treatments.
Principal investigator Professor Diana Eccles said: "There is some evidence in laboratory experiments and observations in humans that BRCA1 gene carriers in particular may be more sensitive to certain types of chemotherapy.
"If the outlook is more optimistic than might be expected for these patients, this will help in planning future preventive surgical options at the time of breast cancer treatment."
Commenting on the study, Samia al Qadhi, chief executive at Breast Cancer Care, said: "Many younger women with breast cancer are terrified about it coming back, especially when they have seen other family members face the disease.
"This crucial study now gives clear evidence confirming that, rather than a family history, it is the type and stage of the breast cancer and the treatments given which are the biggest factors influencing each person's survival.
"It's also important to remember that spotting the signs early is vital - diagnosing breast cancer as soon as possible can lead to simpler and more effective treatment."
Anyone concerned about breast cancer and risk can call Breast Cancer Care on 0808 800 6000.