The company reported a 59% fall in pre-tax profit to £61m in the six months to the end of June 2012 - down from £151m over the same period last year.
G4S faced intense criticism after it failed to meet its £284m contract to provide 10,400 staff for London 2012.
Thousands of military personnel had to be called in - including Army, Royal Navy and Royal Air Force staff - after the company only managed to deliver 83% of its contracted shifts.
But the amount of troops and police officers on duty is due to scaled back for the Paralympic Games - which begin tomorrow - after organisers confirmed that G4S will provide the majority of security for the venues.
Locog chief executive Paul Deighton said he was "fully confident" the private firm would deliver enough staff.
"The military contingent this time will be 3,500 soldiers, with 1,000 in reserve and typically G4S will be between four and 5,000," he said.
"In very simple terms, we're switching from an approach which had a slight majority of military during the Games to one which will have a slight majority of private sector security for the Paralympics."
G4S was also confident looking ahead to the Paralympics, saying it expected to "over-deliver" staff.
The £50m it has set aside as a loss on the Olympic contract is an estimate, and takes into account the cost of military and police deployment and contractual penalties, the company said.
It has begun an internal review into the contract failure, with the findings due to be made public towards the end of September.
Chief executive Nick Buckles said: "We are deeply disappointed that we had significant issues with the London 2012 Olympics contract and are very grateful to the military and the police for their support in helping us to deliver a safe and secure games."
The company, which employs more than 650,000 people, also said restructuring will result in the reduction of 1,100 jobs - fewer than 100 of which will be in the UK.
Some investors had feared the Olympic contract problems would hurt the group's prospects for Government work looking ahead.
Mr Buckles confirmed the costs involved in sorting out the debacle meant the company withdrew from bidding for a Department for Work and Pensions contract worth £20m a year.
But he added no contracts had been lost as a result of the Olympic deal and insisted the company would continue to play a "major role" in the public sector.
G4S' share price fell 2% to 260p after the results were announced.