The crackdown on bogus students and colleges is part of David Cameron's drive to bring net immigration down from more than 200,000 to tens of thousands annually by 2015.
But the reforms will cost the UK £2.4 billion, an impact assessment released by the Home Office showed.
Costs of £3.6 billion will include £2 billion from a "reduced output from students and their dependants" who will no longer be able to come to the UK and from tighter control of foreign students' ability to work in the UK, the assessment said.
A further £170 million cost will come in the loss of student tuition fees to institutions, while the reduced output from post-study workers will cost £1.2 billion.
The UK Border Agency is also expected to see a £160 million loss in income from fees.
But the moves will also bring benefits of £1.1 billion.
Overall, the assessment said the "best estimate" was that the reforms would cost £2.4 billion, but this could be up to £3.6 billion in the worse case scenario.
Immigration Minister Damian Green said: "We are radically reforming the immigration system to tackle abuse and bring net migration down to sustainable levels.
"These changes to the student visa system will create a system where every student coming to the UK attends a legitimate course at a legitimate institution.
"They will work alongside our other reforms of the work route and changes being planned for the settlement and the family routes."
The impact assessment also showed there will be 273,000 fewer student visa grants over the full five years of the parliament, leading to a fall in net migration of about 232,000.
The reforms will also save £75 million in reduced course provision for the education sector, £150 million in reduced UKBA processing costs, and £840 million in reduced costs for public services.
Savings in enforcement costs will also save £45 million "which may be used to combat more significant abuses of the immigration system that potentially result in harm to the UK economy and society", the assessment said.
A UKBA spokesman said: "These proposals will lead to savings of £1.1 billion most of which will benefit our public services.
"It may be there will be even greater benefits as it is not unreasonable to assume that jobs not taken by migrant students will instead be taken up by British workers.
"However, we have costed a worst-case scenario while the Migration Advisory Committee looks at this issue over the summer."
Mrs May has said the "radical" clampdown would close fake colleges and block entry for those who cannot speak good English.
There will also be tougher restrictions on non-EU students staying in the country after their course finishes.
Since the new Government came to power in May last year, 33 educational providers have had their licences revoked for abuses.
Immigration Minister Damian Green said: "These figures show that this Government will not hesitate in taking action against educational providers who do not abide by our rules."
Later, a Home Office spokesman added: "We are required to provide impact assessments, but the process for these assessments is unsatisfactory.
"For example, they require us to assume there is a zero displacement effect of students taking jobs on the local labour market and so we have asked the independent Migration Advisory Committee to look at this issue over the summer."
Pam Tatlow, chief executive of university think-tank million+, said: "The impact assessment sets out the huge cost to the UK of the changes to student visas.
"This is exactly what vice-chancellors and universities have been warning Government about for months.
"At a time of economic difficulty, we should not be introducing reforms that will damage the UK or stop us attracting the talent and skills we need to rebuild our economy.
"Of course we should be doing more to crack down on bogus colleges, but the system did not need the Government to take a sledgehammer to it. The end result could be a catastrophic loss of education exports."
Shadow home office minister Shabana Mahmood said: "The Government's immigration policy is in disarray and they are not being honest about their policies, nor the effect they will have on net migration.
"In getting to this point, the Government has succeeded in damaging the reputation of UK universities as well as our global reputation."
She went on: "We know too from recent reports that the Government is failing to ensure the UKBA has the resources it needs to maintain effective enforcement measures, which is crucial to ensuring students do not overstay their visas.
"We need to crack down on bogus colleges but the Government rhetoric does not match the reality on the ground.
"At the heart of their policies is chaos, confusion and a failure to protect both the UK's border and the economy. The Government has been talking tough on immigration, but it is now clear that they are failing to deliver."
Shadow universities minister Gareth Thomas added: "This decision is not only set to cost Britain over £2.4bn just when we can least afford it, but it will also make it far harder for our universities to fight off competition from the best American universities for the brightest overseas students."
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