Home Office minister Lord Falconer said he was confident the changes would help to avert a repeat of last summer's fiasco, in which thousands of pupils had to be sent home because of delays in vetting new school staff.
The overhaul will alter the role of the 7,000 registered organisations, which include local authorities, independent schools and supply agencies.
These groups will be made to take full responsibility for verifying job applicants' identities later this year. They will also lose their registration if they send in only a small number of applications.
The Independent Schools Council said it was concerned that many schools could lose the ability to apply for checks themselves because they do not take on enough staff each year. The council is considering setting up a system to enable it to apply for checks on schools' behalf, but fears it could be bureaucratic.
Meanwhile, some LEAs fear the changes will add to their costs. Essex County Council still had 1,878 staff in education and children's services awaiting vetting in January and is now considering employing extra staff to double-check the identities of applicants.
Iris Pummell, cabinet member for education, said: "It should be the responsibility of the CRB, but they've had problems so they are just passing it on to the LEAs. We don't have the money to sort this out."
David Hart, general secretary of the National Association of Head Teachers, warned that the bureau still appeared to be unprepared to deal with this year's teacher recruitment round, despite the changes.