The official investigation into the relaxation of border checks last year found border staff went "over and beyond" any scheme approved by ministers, Mrs May said.
The head of the UK border force, Brodie Clark, quit his 40-year career in the Home Office in November amid the row over lax border security.
The border force, part of the UK Border Agency (UKBA), needs a "whole new management culture" and will be split from the UKBA from March, Mrs May said.
She added that Wiltshire Police Chief Constable Brian Moore will be appointed as the new head of the border force.
Mrs May said the report found security checks were suspended without permission, millions of pounds were spent on technology which went unused and briefings were inaccurate.
John Vine, the independent chief inspector of the UKBA, launched his investigation after it emerged the UK's border checks were being relaxed at ports and airports without ministerial approval.
Mr Clark admitted using guidance designed for health and safety emergencies to suspend fingerprint checks at the UK's ports, actions which had no ministerial authorisation, but accused Mrs May of blaming him for "political convenience".
He insisted he was "no rogue officer" and launched a constructive dismissal case in which he could net £135,000.
Publication of the report was delayed last month after Mr Vine asked for more time to complete his investigation.
Mrs May said: "The Vine report reveals a Border Force that suspended important checks without permission; that spent millions on new technologies but chose not to use them; that was led by managers who did not communicate with their staff; and that sent reports to ministers that were inaccurate, unbalanced and excluded key information.
"The Vine report makes a series of recommendations about how to improve the operation at the border, and I accept them all."
She went on: "I do not believe the answer to the very significant problems exposed in the Vine Report is just a series of management changes.
"The Border Force needs a whole new management culture.
"There is no getting away from the fact that UKBA, of which the Border Force is part, has been a troubled organisation since it was founded in 2008.
"From foreign national prisoners to the asylum backlog to the removal of illegal immigrants, it has reacted to a series of problems instead of positively managing its responsibilities.
"With a new chief executive and a plan for comprehensive change, I believe that UKBA is in better hands for the future.
"But I also believe that the extent of the transformational change required - in the agency's caseworking functions and in the Border Force - is too great for one organisation.
"I can therefore tell the House that from March 1, the UK Border Force will be split from UKBA and will become a separate operational command, with its own ethos of law enforcement, led by its own Director General, and accountable directly to ministers."
"The Vine Report reveals that security checks carried out at the border have been suspended regularly and applied inconsistently since at least 2007," Mrs May said.
Checks against the Home Office Warnings Index were not carried out on about 500,000 European Economic Area (EEA) nationals travelling to the UK on Eurostar services from France, Mrs May said.
"These Eurostar passengers are judged to be low risk and they still had their passports checked. But the fact remains that these suspensions were completely unauthorised and that is simply not acceptable."
She added that the report also found that Secure ID, the system for checking the fingerprints of foreign nationals who require a visa to come to Britain, "was suspended on a number of occasions without ministerial approval".
Adding that around 100 million passengers enter the UK each year, Mrs May went on: "The Vine Report is clear that the risk to the border needs to be kept in perspective.
"No one was waved through; everyone had their passports checked; and warnings index checks were almost always carried out so that those who had previously come to the attention of the authorities would still be identified and refused entry."
Mrs May added that the Vine report also uncovered Operation Savant, a local initiative at London's Heathrow Airport, in which students from supposedly low-risk countries were allowed to enter the UK even when they did not have the necessary entry clearance.
"There was no ministerial authorisation for this activity," Mrs May said.
"The report finds that Operation Savant, as it was called, was potentially discriminatory and unlawful.
"The Home Office Permanent Secretary is undertaking a review of this activity and will decide whether any disciplinary action should follow. That review will report by the end of March."
The Home Secretary said an operating policy on the use of Secure ID fingerprint checks will be issued shortly, followed by a new operating mandate for border control.
"This will detail the minimum level of mandatory checks for all passengers; it will set out which additional checks apply to which groups of passengers; and it will cover the opening of chips on passports, interviews for visa holders and the use of Secure ID," Mrs May said.
"It will detail explicitly the additional checks that border officers can apply at their discretion; it will specify the record-keeping standards to be maintained; and it will make clear that no unauthorised suspension of checks is acceptable under any circumstances."
Warning index checks were suspended on 354 occasions, a frequency which "was too high and is likely to have been higher than either the Agency or Ministers anticipated when the policy was introduced", Mr Vine said in his report.
Secure ID checks were also suspended a total of 482 times between June 2010 and November 2011, including 463 times at Heathrow alone, and most of these were between one and four hours.
"These suspensions ranged from a matter of minutes to several hours and were applied regularly, primarily at Terminals 3 and 4."
And between January and June 2011, prior to the introduction of a pilot which relaxed border checks in specific situations, "the biometric chip reading facility had been deactivated on 14,812 occasions at a number of ports".
The UKBA "was unable to explain definitively why these deactivations occurred," Mr Vine said.
Mr Vine went on: "On the basis of the evidence provided to this investigation, it is apparent that the agency does now have a much stronger grip in respect of border security checks than was previously the case.
"However, there remains a question about whether this approach can continue during periods of greater passenger volume, including during the Olympic and Paralympic Games in the summer of 2012."
PA
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