The shock figures sparked accusations that Government drug policies have been "a complete and utter failure" and there are fears that addicts have simply been allowed to become dependent on substitute drugs at vast cost to the NHS.
A drug treatment charity also said using methadone or other drug substitutes was best on a time-limited basis to get addicts off heroin, and said prescriptions "should not become an end in itself".
Recent figures showed that methadone costs the NHS 235m a year – the same as the annual salary of 11,000 nurses – and these figures will add to concerns over the effectiveness of drug treatment at a time when budgets are under intense strain.
Andrew Griffiths, the Tory MP who uncovered the figures and secretary of the all-party group on drug misuse, called for a greater focus on getting addicts clean of drugs. He said: "This shows Government drug policies have been proven to be a complete and utter failure.
"For too many years we've parked people on state induced dependency with methadone, rather than trying to tackle their addiction and get them drug free.
"That's why I think we need a fundamental change in the way we help drug addicts and a move away from the failed policies of the past."
According to the official figures, 7,688 people in Yorkshire and Humber had been receiving "substitute prescribing" such as methadone for more than three years.
That is 16 per cent of the national total of 47,867 who have been on the substitute for such a lengthy period.
As a region, only the north-west has had more addicts on methadone for three years – with 11,400. Even London, with 4,723, has fewer people than in Yorkshire according to the most recent figures, which cover 2009/10.
However, the NHS claims that the numbers on methadone for more than three years are higher in Yorkshire because there are more people who have been in treatment for more than three years.
The Government says 207,000 people across the country needed drug treatment in 1009/10, with 154,000 of them receiving methadone or other substitute drugs which are said to help addicts control and then conquer their addiction. But critics say that methadone is just as addictive as the drug itself.
Simon Antrobus, chief executive of drug charity Addaction, said: 'The figures in Yorkshire and Humber are clearly much higher than elsewhere in the UK, and this is cause for concern. Substitute prescribing, such as methadone, is an important and effective option for helping people with severe heroin problems to recover from their addiction.
"Its use is most effective, in our view, as part of time-limited recovery. ]
"This approach helps stabilise users and takes them away from criminal activity, but also aims to get them free of drugs altogether. The prescription of substitute medication should not become an end in itself."
Historically, some addicts prescribed methadone have been known to sell it on to buy the heroin they prefer, or to mix it with other drugs.
Ministers want an overhaul of the drug treatment system, with more people going into residential rehabilitation and fewer being issued with methadone.
A new strategy announced last year included plans for addicts to lose benefits if they did not co-operate with treatment, while a network of former addicts could be set up to help users overcome their dependency.
Health Minister Anne Milton said: "The goal of all treatment is for drug users to achieve abstinence from their drug (or drugs) of dependency.
"However, there is no single form of drug treatment that is effective for all people with opioid dependence and access to a wide range of treatment options is required to respond to the varying needs of problem drug users.
"The total number of adults in contact with treatment services in 2009-10 was 207,000."
A spokeswoman for NHS Yorkshire and Humber has defended the region's position, however, stating the authorities followed NHS guidance: "Treatments using prescribed substitutes are in line with national guidance which is evidence-based."
In terms of the figures for those who have been on methadone for three years, she said: "We're on a par with the national average".