Mrs May said there will also be a new minimum salary of £40,000 for firms using intra-company transfers (ICTs) to bring their own people into the UK for more than a year to do specific jobs.
But firms will still be able to bring non-EU workers into the UK on ICTs for less than 12 months as long as they earn £24,000.
To fulfill the Government's pledge to cut net migration from 196,000 to the tens of thousands by 2015, Mrs May said: "We will have to take action across all routes to entry - work visas, student visas, family visas - and break the link between temporary routes and permanent settlement."
The number of skilled workers with job offers, who enter the UK on tier two visas under the points-based system, will be capped at 20,700 and will also be limited to graduate-level jobs, Mrs May said.
But the number of highly-skilled workers without a job offer - the old tier one route - will be limited to just 1,000 and to those with "exceptional talent", which will include sports people and scientists.
The inclusion of scientists in this new route will help address the concerns of universities who fear that the cap could make it harder for the UK to attract the world's best researchers.
Speaking in the Commons, Mrs May said: "The old tier one - supposedly for the best and the brightest - has not attracted highly-skilled workers.
"At least 30% of tier one migrants work in low-skilled occupations such as stacking shelves, driving taxis or working as security guards and some don't have a job at all.
"So we will close the tier one general route.
"Instead, I want to use tier one to attract more investors, entrepreneurs and people of exceptional talent."
Mrs May also said student visas would be targeted by the Government.
"Nearly half of all students coming here from abroad are actually coming to study a course below degree level and abuse is particularly common at these lower levels - a recent check of students studying at private institutions below degree level showed that a quarter could not be accounted for.
"Too many students, at these lower levels, have been coming here with a view to living and working, rather than studying. We need to stop this abuse."
Mrs May went on: "Today's announcement has set out a clear, rational approach to which workers we will allow into the UK job market.
"We have set out an approach which will not only get immigration down to sustainable levels but at the same time, protects those businesses and institutions which are vital to our economy."
Unite, the UK's largest union, accused the Government of missing a golden opportunity to root out abuse and misuse by companies of the ICT route.
Peter Skyte, Unite national officer, said: "The Government has spectacularly squandered the opportunity to deal with misuse and abuse of the intra-company transfer scheme in its migration cap announcement in the face of largely empty threats by big business to withdraw investment from the UK.
"The measures announced will do little to prevent employers from abusing the system, and manipulating tax and accommodation allowances to undercut UK resident workers.
"The Government has also failed to take any action to stimulate job opportunities to reduce the high unemployment rate for skilled computer science graduates and young people in general by providing employers with greater incentives to source labour from the domestic market as envisaged in its original consultation on the migration cap."
John Mountford, international director of the Association of Colleges, warned that non-EU students coming to the UK on courses below degree level "subsidise UK universities and UK students" by going on to degrees later.
"Cutting them out will ultimately mean that UK citizens will have to pay even more for a university degree," he said.
"The cap is a clumsy approach - to cut numbers most effectively the Government should simply administer current policy properly.
"This would reduce student numbers by removing bad practice, clamping down on 'chip shop' providers while supporting highly trusted providers like Further Education and Sixth Form Colleges, which specialise in high-quality education to genuine students.
"Introducing a cap will punish reputable providers to the benefit of the bad, as the unscrupulous will continue to look for loopholes."
"Restricting student numbers in this way will harm UK economy and reputation.
"Students turned away from the UK will study in America or elsewhere in Europe and our reputation as an international educator of excellence will be severely damaged."
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