Sajid Javid will unveil a major easing of Britain's immigration system that will enable thousands more highly-skilled migrants to come to the United Kingdom in the run-up to Brexit, The Telegraph has learned.
The cap was set by Mrs May when she became home secretary in 2010.
The number of Tier 2 visas granted to skilled workers outside the EEA and Swizerland is limited to 20,700 people a year.
Number 10 played down suggestions that the Government was moving away from its target to get annual net migration below 100,000, stressing that the Prime Minister remains committed to reducing the number to "sustainable" levels. NHS England had 35,000 nurse vacancies and almost 10,000 doctor posts unfilled in February.
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 proposed changes will affect the Tier 2 visas, which are used by skilled workers from outside the European Economic Area and Switzerland.
Earlier in the month, Practice Business reported on home secretary Sajid Javid's BBC interview, in which he said he hoped to review the immigration policy with regard to the tier 2 visa cap restricting worldwide doctors from working in the UK.
Indian doctors have always been the second largest group in the NHS, after those who qualified in the UK.
Cordery said: "This is going to be a huge relief for trusts up and down the country who have been really struggling to fill their doctors and nurses vacancies".
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.
At the start of June, Mr Javid signalled there could be a softer approach to immigration policy under his leadership at the Home Office, including looking again at the cap on "tier two visas". That is why I have reviewed our skilled worker visa route.
The Telegraph reported that a number of Cabinet ministers had joined Mr Javid to convince the Prime Minister to exclude medical staff from the tier two cap.
'This builds on steps we have already taken to make sure the NHS has the staff it needs for the future - boosting training places for home-grown doctors and nurses by 25% and giving over a million NHS employees a well-deserved pay rise'.
The removal of doctors and nurses from the Tier Two total will have the knock-on effect of freeing up hundreds of places each month for other professions, including engineers, IT professionals and teachers.
"It's the right short-term fix for 2018".