The move, which will apply to all European union members, is designed to give patients greater freedom and ease congestion in countries that have long waiting lists for operations.
Previously, patients who chose to pay for better or quicker treatment abroad had to mount legal action to make the NHS reimburse them.
But an EU directive on cross-border healthcare, to be published on Wednesday, will let patients shop around freely in all 27 member states.
It means British patients would have the right to seek any treatment offered by the NHS, such as cancer care or hip replacements, anywhere which could provide it more quickly.
Patients would have to pay upfront where they were treated, but as long as the cost was lower than in the NHS, they could reclaim it in full.
A European Commission spokesman said: "In the week the NHS marks its 60th anniversary, the European Commission will publish draft legislation on the application of patient's rights in cross-border healthcare.
"The proposal will clarify and promote the right of patients to get healthcare treatment in another EU country, as well as provide a basis for increased cooperation between EU healthcare systems."
The attraction for British patients is clear as although waiting lists have fallen under Labour, they are still longer in many other countries.
NHS hospitals also have a higher incidence of superbugs and poorer survival rates for many conditions, including some cancers, than their foreign counterparts.
Experts have predicted that these reasons mean it is unlikely there will be an influx of foreigners to the NHS.
The plan could threaten the stability of NHS finances, however, as the health service will lose revenue to hospitals overseas.
There is also serious concern about Britons living abroad charging the NHS for all their medical care. Currently, many rely on private medical insurance to cover local treatment.
Under the draft proposals the NHS would be obliged to fund all overseas outpatient treatment - such as scans and minor operations - even where patients do not seek authorisation beforehand.
But Health Secretary Alan Johnson is fighting for the right to make patients obtain NHS permission in advance for major operations.
The health department said: 'We are absolutely committed to ensuring that the NHS retains the ability to decide what care it will fund.'
Doctors' leaders said the move would encourage the NHS to improve standards, but warned that "health tourism" would most likely only appeal to the wealthy and well-educated.
Dr Terry John, chairman of the BMA's international committee, said: "Standards of care for people who choose to stay in their home country, or are unable to travel abroad, must be maintained."
In 2006 the European Court of Justice first ruled that British patients who face an "undue delay'' for treatment at home can be reimbursed if doctors agree that treatment abroad is justified because of pain, disability or other pressing medical needs.
That battle was begun by Yvonne Watts, 76, who went to France for a hip replacement in 2002.
Her local health service, Bedford Primary Care Trust, had refused to pay her £4,000 bill.
