Those placed on the sex offenders register for life can now argue their case for removal, in accordance with a 2010 High Court ruling.
The law change means that people who have been convicted of sex crimes against an adult or a child could have their name struck from the register.
Offenders will have to wait 15 years after release from prison before they can appeal, as ministers said they would make the minimal amount of changes possible to comply with the law.
Home Secretary Theresa May previously said she was "appalled" by the decision, while the Labour opposition also disagreed with the ruling.
Joining them were charities such as the NSPCC, which said paedophiles on the register should always remain on the list.
"There is no proven or recognised 'cure' for adult sex offenders who abuse children and they must therefore always be considered a risk," the charity's chief executive, Andrew Flanagan, said.
"Physical and emotional harm caused by sexual abuse can damage children's lives.
"We will monitor the appeals process closely and will raise concerns if we believe the civil liberties of convicted sex offenders are being put before the protection of children."
However, a Home Office spokesperson told the BBC it will do everything in its power "to protect the public from predatory sex offenders".
"The review process for offenders is robust and puts public protection first. It also prevents sex offenders from wasting taxpayers' money by repeatedly challenging our laws," he said.
"Sex offenders who continue to pose a risk will remain on the register for life."Suggest a correction