Project Prevention is offering to pay £200 to any drug user in London, Glasgow, Bristol, Leicester and parts of Wales who agrees to be operated on.
The first person in the UK to accept the cash is drug addict "John" from Leicester who says he "should never be a father".
The move has been criticised by some drug charities who work with addicts.
Project Prevention founder Barbara Harris admitted her methods amounted to "bribery", but said it was the only way to stop babies being physically and mentally damaged by drugs during pregnancy.
Drug treatment charity Addaction estimates one million children in the UK are living with parents who abuse drugs.
Pregnant addicts can pass on the dependency to the unborn child, leading to organ and brain damage.
Mrs Harris set up her charity in North Carolina after adopting the children of a crack addict.
Damage to children
Speaking to the BBC's Inside Out programme, she said: "The birth mother of my children obviously dabbled in all drugs and alcohol - she literally had a baby every year for eight years.
"I get very angry about the damage that drugs do to these children."
After paying 3,500 addicts across the United States not to have children, she is now visiting parts of the UK blighted by drugs to encourage users to undergo "long-term birth control" for cash.
John, a 38-year-old addict from Leicester, is the first person in the UK to accept money to have a vasectomy after being involved in drugs since he was 12.
He said: "It was something that I'd been thinking about for a long time.
"I won't be able to support a kid; I can just about manage to support myself."
Simon Antrobus, chief executive of Addaction, said while no-one wanted to see children brought up in a drug-using environment, there was no place for Project Prevention in the UK.
"It exploits very vulnerable people who are addicted to drugs and alcohol at probably the lowest point in their lives," he said.
The Reverend Robert Black, of Victory Outreach, which works with former addicts in east London, said he thought Project Prevention's aims were "very devious".
Maria Cripps, project manager at the Hackney Dovetail Centre which works with drug users and their carers, said: "I think Barbara uses some very extreme examples to get her point across. It might work in America but Great Britain is a very different country."
But Reverend Martin Blakebrough, director of Camden's Kaleidoscope Project in north London, said sterilisation was "worth considering" if it was right for the individual.
A spokesperson at the British Medical Association said: "The BMA's ethics committee does not have a view on the charity Project Prevention.
"As with all requests for treatment, doctors need to be confident that the individual has the capacity to make the specific decision at the time the decision is required.
"The BMA's ethics committee also believes that doctors should inform patients of the benefits of reversible contraception so that the patients have more reproductive choices in the future."