The report, seen by the BBC, was commissioned by the oil minister in the wake of this year’s fuel protests to probe the financial side of the sector.
It says $29bn (Â£18bn) was lost in the last decade in an apparent price-fixing scam involving the sale of natural gas.
It also calculated the treasury loses $6bn a year because of oil theft.
Nigeria is one of the world’s biggest oil producers but most of its people remain mired in poverty.
The Petroleum Revenue Special Task Force report is one of several commissioned by the government – and follows an outcry after a parliamentary investigation uncovered a massive multi-billion fuel subsidy scam.
That had been set up after angry nationwide protests in January when the government tried to remove a fuel subsidy.
Earlier this week, a campaign was launched to clean up Nigeria’s oil sector.
It was led by Patrick Dele Cole, a politician from the oil-rich Niger Delta region, who said that 90% of the stolen oil was refined in eastern Europe and Singapore.
The BBC’s Will Ross in Lagos says this leaked report exposes the extent of the rot in Nigeria’s oil and gas industry – all the way from the awarding of contracts to the sale of refined products.
It is staggering just how much money the people of Nigeria appear to be missing out on, he says.
Nigeria’s Oil Minister Diezani Alison-Madueke declined to comment on the specifics of the probe but said a report compiled from several committees set up earlier in the year to investigate the oil and gas sector was in its final stages and would be presented to the president soon.
The Petroleum Revenue Special Task Force, headed by former anti-corruption chief Nuhu Ribadu, revealed in its report that losses of revenue to the treasury over apparent gas price-fixing involved dealings between Total, Eni and Shell and government officials.
The report does not suggest the companies broke the law but called for measures to be put in place to ensure all transactions are more transparent.
It said that oil and gas companies owe the treasury more than $3bn in royalties.
For the period 2005 to 2011, it said $566m was owed in signature bonuses – the fees a company is supposed to pay up front for the right to exploit an oil block.
The report looked at the issue of discretionary licences which companies do not have to bid for.
Between 2008 and 2011 it found the Nigerian government had handed out seven discretionary licences, from which $183m in signature bonuses had not been paid.
A Shell spokesman said the company would not comment as it had not yet seen the report.
Our correspondent says it is well known that oil theft is a major problem in Nigeria, but the report says it may be reaching emergency levels as 250,000 barrels of crude oil could be being stolen every day – 10% of annual production.
The leaked report said that small-scale “pilfering” had been “endemic since at least the late 1990s”, but it also said it had heard allegations about thefts from crude export terminals, tank farms, refinery storage tanks, jetties and ports.
“Submissions to the Task Force alleged that officials and private actors disguise theft through manipulation of meters and shipping documents,” the report said.
“Yet there is also evidence that members of the security forces condone and, in some cases, profit from theft. The void in effective security likewise appears to increasingly hand over control of coastal and inland waterways to undesirable elements.”
The investigation showed that 40% of refined products – either refined in Nigeria or imported – currently being channelled through state-owned pipelines are lost to theft and sabotage.
Mr Ribadu’s investigation calls for a total overhaul of the industry with an oil sector transparency law requiring all companies to report all payments and publish all contracts and licences.
The Task Force also wants a special financial crimes unit to be established specifically for the oil and gas sector.