Eradication efforts were seen as inefficient because too little was being destroyed at too high a cost, Antonio Maria Costa, the UN drug chief, said.
The old policy was unpopular among powerless small-scale farmers, who often were targeted in the eradication efforts.
Highs and lows
Afghanistan is the world's leading source of opium, cultivating 93 per cent of the world's heroin-producing crop.
While opium cultivation fell 19 per cent last year, it remains concentrated in Afghanistan's southern provinces where the Taliban earned an estimated $50 million to $70 million, according to the UN drug office.
The new policy calls for assisting farmers who abandon poppy cultivation.
Holbrooke said the international community was not trying to target Afghan farmers, just the Taliban who buy their crops.
"The farmers are not our enemy, they're just growing a crop to make a living," he said.
"It's the drug system. So the US policy was driving people into the hands of the Taliban."
Holbrooke said that Washington is increasing its funding for agricultural assistance from tens of millions of dollars a year to hundreds of millions of dollars.
"We're essentially phasing out our support for crop eradication and using the money to work on interdiction, rule of law, alternative crops," he said.
Reacting to the US announcement, a senior Afghan official said that his government agrees with Holbrooke's assessment .
"We are happy with the [new] policy," Mohammad Zafar, the Afghan deputy minister of drugs and anti-narcotics, told Al Jazeera on Sunday.
"Once the farmers get more support then they will leave cultivation of drugs in their fields, because they will have another type of alternative livelihood.
"If we control the drug trafficking, the drug trade, then the price of the opium will be reduced and nobody will go back to cultivating drugs.
"At the same time, if we provide support to the farmer, it will reduce the drug problem in Afghanistan."
The new US policy also calls for co-ordinating a crackdown on drug trafficking across Afghanistan's border before the heroin reaches addicts in Europe, Russia and Iran.
In recent months, US and Nato troops in Afghanistan have begun attacking drug labs and opium storage sites in an effort to deprive the Taliban of drug profits.
In 2007 193,000 hectares of opium was cultivated. In 2008 the number has dropped by 19 per cent to 157,000 hectares.
But opium production declined by only 6 per cent to 7,700 tonnes from 2007 to 2008.
Since 2007, the number of opium-free provinces has increased by almost 50 per cent, from 13 to 18.
98 per cent of all opium is grown in just seven provinces in the south-west where there are permanent Taliban settlements.
In Helmand province, in the south, 103,000 hectares of opium were cultivated in 2008 year – two thirds of all opium in Afghanistan.
In 2007, 19,047 hectares of opium was eradicated. In 2008 only 5,480 hectares were eradicated.
Source: UN Office on Drugs and Crime
According to a UN report this week, opium eradication reached a high in 2003, after the Taliban were removed from power, with over 21,000 hectares destroyed.
In 2008, only 5,480 hectares were cut down, compared with 19,047 hectares in 2007.
The UN's Costa said Afghan opium would kill 100,000 people this year in the parts of world where demand for heroin is highest - Europe, Russia and West Asia.
To fight it, he said, major powers have to expand their counter-drug efforts to neighbouring Pakistan as well as Iran, where half the 7,000 tonnes of exported Afghan opium transits, "causing the highest addiction rate in the world".
"Facing a grave health epidemic, Iran should be given the chance to engage in common efforts to combat illicit trafficking," Costa said.
Iran had been invited to attend the G8 meeting in Italy because anti-drug efforts in Afghanistan have been identified as a vital area where the US and Iran can work together.
But Rome withdrew the invitation when Tehran failed to respond and after its severe crackdown on demonstrators protesting against the country's election result, which has sparked international condemnation.