The news comes with just 15 days to go until the opening ceremony on 27 July. The move will bring the total number of military personnel contributing to the safety and security of the Games to 17,000.
Event reported in January that G4S received 34,000 applications for the 13,700 positions it was tasked to fill in order to safeguard the Games.
The company could now face fines of up to £50,000 per day for not meeting staffing levels.
In a statement, G4S said it "encountered some delays" in its employment and training process. "This is an unprecedented and very complex security recruitment and deployment exercise which is being carried out to a very tight schedule," it said.
"We already have around 4,000 people at work across 100 venues. We currently have over 9,000 additional people going through the final stages of the required extensive training, vetting and accreditation process."
According to the Home Office, the government is confident that it will not exceed the £553m it has committed for venue security at the Games.
Secretary of state for defence Philip Hammond said Army chiefs of staff recognise the importance of the Olympic Games and support the deployment, adding "ministers across government recognise the burden that this additional short-notice deployment will impose upon individual service men and women and their families."
He said: "I can confirm that there remains no specific threat to the Games. Nor is there an increased threat to the games. We are confident that the UK is ready and able to provide a safe and secure Olympic Games for the whole world to enjoy."
A spokesperson from Locog said it does not anticipate an increase in the overall venue security numbers at the Games. "Security for the Games is big and complex but we have the best brains in the security business working on this – Home Office, Metropolitan Police, MoD and world’s largest private security business. Delivering a safe and secure Games is everyone’s number one priority."
Home Secretary Theresa May defended G4S in the Commons earlier this week, saying she was confident the security partners would "deliver a safe and secure Games".
G4S was contracted in March 2011 to recruit, train and manage 13,700 security staff during the Olympic and Paralympic Games to work alongside police and local authorities.
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