Security companies G4S and Serco are to hand over their contracts to electronically tag criminals following fraud allegations over the way they charged the government.

They have been told to hand over all their responsibilities to rivals Capita on an interim basis by the end of March, the justice secretary, Chris Grayling, has said. Capita is one of four companies in the running to take over the service permanently.

Grayling said in a Commons written statement: "We have signed a contract with Capita to take over the management of the existing electronic monitoring services on an interim basis.

"This will mean that management of these services, which are now operated by G4S and Serco, will transition to Capita by the end of the current financial year.

"Under these arrangements, Capita will be using the systems and equipment of G4S and Serco, but the two companies will no longer have a direct role in delivering the service on the ground."

Grayling last month rejected an offer from G4S of a £24.1m "credit note" after it admitted that overcharging on its contract for the electronic monitoring of thousands of offenders had been going on for years.

The Serious Fraud Office has started a full-scale criminal investigation into both companies over their Ministry of Justice (MoJ) contracts.

Serco has co-operated with ministry inquiries since July and said it would refund any agreed overcharges. Some offenders were claimed to be under tagging restrictions but were found to be dead, back in prison or overseas. Both companies withdrew from tagging contracts due to be renewed. Other companies named as preferred bidders for the work are Buddi, Astrium and Telefonica.

Across government there is now in effect a moratorium on Serco or G4S getting any new work. Although they can still bid for contracts, they will not be awarded any unless they are given a clean bill of health over the tagging dispute.

Grayling said on Thursday: "This signals a fresh start for electronic monitoring that brings us a step closer to introducing the most advanced tagging system in the world.

"Monitoring the movements of dangerous and repeat offenders will be vital in cutting crime, creating a safer society with fewer victims and offering greater protection and reassurance to the public."

An audit by PricewaterhouseCoopers, launched in May, alleged that overcharging began at least as far back as the start of the current contracts in 2005.

Serco, which announced in July that it would not be bidding again for the tagging contract, said it had been working with the MoJ and Capita "to ensure a smooth and effective transfer of the contract".

Grayling said the current contracts were due to expire at the end of March but he wanted to ensure continuity until new contracts came into effect later in 2014.

G4S said it was not being stripped of its contract. It said it had already withdrawn from it.