LONDON (Reuters) - Britain's Serious Fraud Office said on Monday it had opened a criminal investigation into G4S and Serco's electronic monitoring contracts. The SFO investigators will now decide whether to prosecute the firms charging for tagging criminals under the contracts. In July, the British government placed all contracts held by G4S and its rival Serco under review after an audit showed they charged for tagging criminals who were either dead, in prison or never tagged in the first place. The government then asked the SFO to consider carrying out an investigation into G4S tagging contracts. It later referred Serco in September. Serco's Chief Executive Chris Hyman quit last month as part of a major reorganization aimed at rebuilding the company's reputation with the British government, from which it gets a quarter of its annual revenue. G4S, the world's biggest security firm, gets around 10 percent of its annual revenue from the British government. Its Chief Executive Nick Buckles and UK head Richard Morris have both quit since the scandal first broke in May. Both firms have said they would repay any amount and also pulled out of a retender for the contract, which analysts have estimated is worth up to 150 million pounds. G4S said on Monday it would co-operate fully with the SFO investigation. Serco could not be immediately reached for comment. Shares in G4S were down 2.08 percent to 249.7, while Serco's shares were down 0.37 percent by 6.30 a.m. ET. (Reporting by Neil Maidment; Editing by Rhys Jones and Jane Merriman)