The organisation will be split into two new organisations, one to handle immigration and visas, and another to enforce laws.
Reports suggest neither of the new bodies will carry agency status.
In a speech to the House of Commons May blamed the organisations catalogue of problems on the previous government.
The Home Affairs select committee said on Monday that the backlog of cases would take 24 years to clear.
“No sooner is one backlog closed, than four more are discovered. At this rate, it will take 24 years to clear the backlog which still stands at the size of the population of Iceland,” said MP Keith Vaz.
The commons home affairs committee accused Lin Homer, the former UKBA head from 2008 until 2011 of a “catastrophic leadership failure”.
Homer was then given the job of Chief Executive of HM Revenue and Customs on a £180,000 salary.
“UKBA has been a troubled organisation for many years,” May told the Commons.
“It has a poor IT system and operates under complex legal arrangements that often work against it.
“In keeping with the changes we made last year to Border Force, the Government is splitting up the UK Border Agency. In its place will be an immigration and visa service and an immigration law enforcement organisation. By creating two entities instead of one, we will be able to create distinct cultures.
“Two smaller entities will also mean greater transparency and accountability and that brings me to the second change I intend to make. UKBA was given agency status in order to keep its work at an arm’s length from ministers.
“That was wrong. It created a closed, secretive and defensive culture. So I can tell the House that the new entities will not have agency status and will sit in the Home Office, reporting to ministers.
“UKBA was given agency status in order to keep its work at an arm’s length from ministers. That was wrong. It created a closed, secretive and defensive culture,” May concluded.
The split comes just a year after May initiated a split in the previous government body in charge of immigration issues.
The BBC reports that all costs of the proposed reorganisation will be met from within existing budgets allocated to UKBA.
TNT has been campaigning for UKBA reforms – sign our petition here.