The game-changing injections can help people lose more than 10 per cent of their body weight.
It is based on the drug semaglutide, the same ingredient as trendy Ozempic jabs which are in short supply because of massive demand.
Pharma company Novo Nordisk said it will today launch a “controlled and limited” supply of Wegovy.
It was expected to be available in Britain earlier this year but was pushed back.
Ministers want to roll the jabs out much more widely to tackle the UK’s soaring weight problem, with three in 10 adults obese in England.
Up to a massive four million people are thought to be eligible but the plans are on ice because of supply problems.
Novo Nordisk said: “We believe the launch of Wegovy will help provide an additional option to support people living with obesity in the UK.
“It will be available in specialist NHS weight management services for people who meet the criteria or privately through a registered healthcare professional.”
The firm admitted supplies will be “constrained for the foreseeable future”.
Experts say private patients wanting to lose weight and black market sellers are making it hard for the NHS to get hold of the medication.
Sun columnist Jeremy Clarkson and tech mogul Elon Musk have both admitted taking semaglutide in a bid to slim down.
It is only meant to be used for people who are obese and have a weight-linked illness like type 2 diabetes or heart disease.
To get it through the health service patients must also exercise and eat a healthy diet as a combined effort to lose weight.
Scientists say it is important for people to take it long-term – for years – so they don’t pile the pounds back on.
Semaglutide only needs to be injected once a week and it mimics a hormone that makes you feel full, preventing overeating.
Studies have found it can also slash the risk of heart attacks, stroke and even dementia.
The drug regulator NICE approved Wegovy for NHS patients in March.
Director of medicines evaluation, Helen Knight, said: “For some people losing weight is a real challenge which is why a medicine like semaglutide is a welcome option.
“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.”