Resistant strains of bacteria are spreading globally, threatening to make existing drugs ineffective.
A global innovation fund of $2bn over five years would be used to boost funding for "blue-sky" research into drugs and diagnostics - with much of the money going to universities and small biotech companies.
One promising area of research concerns so-called "resistance breakers". These are compounds that work to boost the effectiveness of existing antibiotics - a far less costly approach than attempting to discover entirely new drugs.
Helperby Therapeutics, a spin-out company founded by Prof Anthony Coates, St George's, University of London, has created a resistance breaker that acts against the superbug MRSA.
The compound, known as HT61, will shortly go into clinical trials in India, where it is being developed under licence by Cadila Pharmaceuticals India.
The review team said this kind of research could benefit from the innovation fund and could be the key to making existing drugs last longer.
Mr O'Neill said the big pharmaceutical companies should pay for the fund and look beyond short-term assessments of profit and loss.
Formerly chief economist with the investment bank Goldman Sachs, Mr O'Neill drew parallels between the banking crisis and the looming catastrophe of a world where antibiotics no longer worked. Innovation funding
He said big pharma needed to act with "enlightened self-interest" because "if it gets really bad, somebody is going to come gunning for these guys just how people came gunning for finance".
Mr O'Neill was speaking to the BBC's Panorama programme, which has spent six months following the work of the review team, filming in India, the US and UK.
Mr O'Neill was appointed last year by Prime Minister David Cameron to head the review into antimicrobial resistance - which already claims an estimated 30,000 lives a year across Europe.
Many large companies have pulled out of antibiotic research.
The report says this is partly due to the uncertain commercial returns for new antibiotics.
New drugs are often kept in reserve for years, to preserve their potency, by which time they may be nearing the end of their patent.
After this expires, cheaper generic versions are available.
In order to incentivise drug development, the review team says, there should be lump-sum payments to companies that create proven new antibiotics.
This would break the link between the profitability of a drug and its volume of sales.
The review team predicts its proposals could lead to 15 new antibiotics a decade, of which at least four should be "breakthrough products" targeting the bacterial species of greatest concern.
It estimates the cost of guaranteed payments for these drugs would be $16-37bn over a decade but says this is a small price to pay given that antibiotics are essential to so many aspects of healthcare, from common infections, to surgery and cancer treatment.
US breakthrough
It is nearly 30 years since a new class of antibiotics - meaning a group of drugs with an entirely novel action - was introduced.
But this decades-long drought could be over as a result of a breakthrough recently announced by US scientists.
A team at Northeastern University in Boston, Massachusetts, has discovered 25 potential new antibiotics, all of them derived from soil microbes.
One of them, teixobactin, is effective against both tuberculosis and MRSA.
The drug is being developed by NovoBiotic Pharmaceuticals and should go into patient trials within two years.
Prof Kim Lewis, of Northeastern University, who co-founded the company, told Panorama: "We think there could be thousands more antibiotics in the soil, yet to be discovered."