The National Institute for Health and Care Excellence gave the injections, which are popular among celebrities, approval for NHS use.
Thousands of people are expected to be offered the appetite suppressant Wegovy on prescription.
Experts say the decision to make the drug available on the NHS is a “pivotal moment” for the treatment of obesity, but others warn that the drug is not a “quick fix”.
A previous study found that people who are given the drug, which comes as a weekly injection, had their weight drop by 12 per cent on average after 68 weeks.
The institute has issued final guidance recommending semaglutide (traded as Wegovy and made by Novo Nordisk) for adults with at least one weight-related condition and a body mass index score of at least 35.
The weight-related conditions that make obese people eligible include type 2 diabetes, pre-diabetes, high blood pressure, dyslipidaemia (unbalanced or unhealthy cholesterol levels), obstructive sleep apnoea and heart disease.
In some cases, people with a BMI of 30 and over may be able to access the drug, which is given through a pen injector.
People will only be given Wegovy on prescription as part of a specialist weight management service involving input from several professionals, and for a maximum of two years.
It is to be used alongside a reduced-calorie diet and increased physical activity, the institute said.
Patients inject themselves weekly with the drug, which suppresses the appetite through mimicking the hormone glucagon-like peptide-1 (GLP-1) that is released after eating.
This makes people feel full, meaning they eat less and lose weight.
A previous study, published in the New England Journal of Medicine, found that nausea and diarrhoea were the most common side-effects but these were “typically transient and mild-to-moderate in severity and subsided with time”.
The drug will be available to NHS patients soon, after its launch in England is confirmed by Novo Nordisk.
Th NHS in England is required to implement the institute's recommendations within three months of the product becoming commercially available.
“For some people losing weight is a real challenge, which is why a medicine like semaglutide is a welcome option," said Helen Knight, director of medicine evaluation at the institute.
“It won’t be available to everyone. Our committee has made specific recommendations to ensure it remains value for money for the taxpayer, and it can only be used for a maximum of two years.
“We are pleased to finally publish our final guidance on semaglutide which will mean some people will be able to access this much talked-about drug on the NHS.”
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Alex Miras, professor of endocrinology at Ulster University, said: “This decision made by Nice is a pivotal moment for the treatment of people living with obesity.
“The weight loss that can be achieved with this safe medication is substantial and likely to lead to the improvement of obesity-related complications in a large number of patients.”
Dr Stephen Lawrence, associate clinical professor at the University of Warwick, said: “When used in accordance with the prescribed guidelines, it promotes weight loss in a safe and effective way for most people.
“It is important to note, however, that this medication is not a quick fix or a replacement for following a healthy lifestyle, which includes regular physical activity and healthy eating.
“It should therefore only be offered following assessment of the person taking the medication and as part of a programme to establish a healthy lifestyle.”
Dr Simon Cork, senior lecturer in physiology at Anglia Ruskin University, said: “The news that semaglutide will be available on prescription for the treatment of obesity will be welcome to the millions of people who struggle to lose weight and maintain that lower body weight.
“However, many will be disappointed by the strict rules dictating who will be eligible for this drug.”
Charity Beat raised concerns about the effect of the drug on people with eating disorders.
“Weight-loss medications like semaglutide can be extremely attractive to people with eating disorders as they appear to provide quick results," said Tom Quinn, Beat’s director of external affairs.
“However, these medications can be very dangerous as they can worsen harmful thoughts and behaviours for those unwell, or contribute to an eating disorder developing for someone who is already vulnerable.”
In February it emerged that some high street chemists in England will prescribe the drug, if suitable, through their online doctor services.
“Novo Nordisk welcomes the final Nice recommendation for Wegovy as an option for weight management within the NHS," a company representative said.
“We are working to make Wegovy available in the UK as soon as possible.”