The Justice Minister says the electronic tagging of repeat offenders will cost €3,000 a year, per tag, in operation.
Frances Fitzgerald brought the bill to Cabinet this morning.
She says it will provide more security to the victims of serious crimes, but lobby groups have raised concerns over whether electronic tagging actually prevents crime.
Minister Fitzgerald says Gardaí will monitor the electronic tagging.
"It's a targeted initiative for those judged to be at most risk of offending while on bail.
"If they remove the tag or whatever they'll be in breach of bail and gardaí can get a warrant for their arrest and the gardaí will be monitoring and operating this."