The Royal College of General Practitioners (RCGP) said Thursday's announcement would be a "much-needed victory for common sense and patient care".
Sajid Javid will remove non-EU doctors and nurses from the annual 20,700 "tier 2" visa limit on non-EU workers, the Sun and the Telegraph reported on Wednesday.
The cap was introduced by PM Theresa May when she was the home secretary.
Earlier this month, family doctors had also urged Javid to lift the cap warning of a "desperate need" to ease pressures amid escalating patient demand.
The British government will relax immigration rules to allow more doctors and nurses from outside the European Union to come and work for the National health service in the UK.
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He said he would take "think more carefully" about the cap on the number of skilled workers given visas.
"The NHS, general practice included, has always been supported by the skills and hard work of doctors and other healthcare professionals from overseas".
The BMA said a change in the rules would "be welcome relief to doctors and patients, who have witnessed first hand the damage that this policy has caused".
As part of a long-term government plan for the NHS, more details of which will be set out in due course, doctors and nurses are to be excluded from the cap on skilled worker visas.
The move would mean businesses will be allowed to employ an additional 8,000 skilled migrants annually in industries including IT, engineering and education, which according to the paper effectively increases the current cap by 40 percent.
" "La France accueillera des migrants de l'" Aquarius ", annonce l'Espagne
L'Italie a indiqué qu'elle jugeait " inacceptables " les critiques de la France sur son attitude dans l'affaire de l'Aquarius . La visite du ministre de l'Économie, Giovanni Tria, qui devait rencontrer Bruno Le Maire à Paris mercredi, a été annulée.
Sunder Katwala, director of the immigration think-tank British Future, described the expected announcement as a "sensible move". NHS England had 35,000 nurse vacancies and almost 10,000 doctor posts unfilled in February.
The home secretary will also announce a review, to be conducted by the Migration Advisory Council, of the professions that qualify for the visas, with a view to adding Global Positioning System and teachers, among others. In the longer term, Britain will need better training of doctors, engineers and others here in the United Kingdom, together with an immigration system that welcomes people with the skills we need.
Home secretary Sajid Javid, who promised to put in place a fairer immigration system instead of what is called the policy of "hostile environment", said: "I recognise the pressures faced by the NHS and other sectors in recent months".
Meanwhile, MPs have attacked the Home Office for threatening to deport migrant workers for making amendments to their tax records.
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