"We have not seen a truly new class of antibiotics for decades," said Lord O'Neill.
"It's in the policy makers' hands to change this.
"We have recommended that countries must review carefully how they buy and price antibiotics, to reward innovative new drugs without encouraging unnecessary use of new antibiotics.
"I call on the governments of the G7, G20 and the UN to take real action in 2016 to avoid the terrible human and economic costs of resistance that the world will otherwise face."
Lord O'Neill pointed out that in the US more than 70 percent of antibiotics defined as medically important for humans are in fact sold for use in animals, a practice he said should be banned or at least severely restricted.
He also called for a return to a traditional mind-set of cleanliness and infection control so fewer antibiotics are needed to fight bacterial infections.
The report argues for "market entry rewards" of around $1 billion each for the successful production of new antibiotics, to be paid for by allocating a percentage of G20 counties' existing healthcare spending.
Lord O'Neill also calls for a new charge on pharmaceutical companies who do not invest in research for AMR, as well as implementing a new tax on antibiotics, to fund the rewards.
Chancellor George Osborne said that without intervention, AMR could pose a greater threat to mankind than cancer.
"Apart from the moral case for action, the economic cost of failing to act is too great to contemplate," he said.
"I am calling on other finance ministers to come together this year and, working with industry leaders and medical experts, agree a common approach."
Professor Dame Sally Davies, Chief Medical Officer for England, said the "golden age" of antibiotics, which the world had taken for granted for more than fifty years, had ended.
"We are already seeing the consequences of AMR, with estimates of around 50,000 deaths per year recently in Europe and the US due to antibiotic resistance infections, and far greater numbers worldwide," she said.
"The projected figures are much more worrying.
"At present, around seven percent of deaths are due to infections.
"If we do not act, this could rise to 40 percent, as it was before we had antibiotics."
Professor Nigel Gibbens, UK Chief Veterinary Officer, said there was now "more than enough evidence" to take action on the use of antibiotics in animal production.