NHS England says inclisiran, given as a twice-a-year injection, could save about 30,000 lives within a decade.
It normally costs nearly £2,000 per dose but Novartis, which makes it, has agreed an undisclosed discount.
It can lower bad fat in the blood when other cheaper drugs, like statins, have not done enough, says draft advice.
The health watchdog NICE is recommending it as an option for people who have already had a stroke or heart attack and are not responding to other cholesterol-lowering treatments.
Experts hope it will help to cut their risk of further life-threatening cardiovascular events.
Although there is no long-term proof of this yet from studies, they believe it is worth recommending based on existing evidence.
It will bring England and Wales in line with guidance for Scotland.
More than two in five people in England are thought to have high cholesterol and around 6.5 million adults are taking medicines, called statins, to help lower it.
Zena Forster, 65, from Newcastle, has had a stroke and a heart attack and been diagnosed with an inherited condition that means her cholesterol levels are always high, despite taking statins.
"I'm on my fourth statin now," she told the BBC One's Breakfast programme.
"Heart disease is relentless and there is no cure - and I just aim to slow the progress."
The new drug was "good news" for people like herself, Ms Forster said, and offered hope as another treatment option.
And taking it twice a year would be no burden compared with remembering to take a daily pill.
While statins - which are taken daily - slow down the production of cholesterol in the liver, inclisiran works in a different way.
It uses gene-silencing to help the liver remove harmful cholesterol.
It turns off, or silences, a gene called PCSK9, which results in the liver absorbing more "bad" LDL cholesterol from the blood and breaking it down.
It can be used on its own or alongside statins.
Meindert Boysen, NICE deputy chief executive and director of the Centre for Health Technology Evaluation, said: "Inclisiran represents a potential game-changer in preventing thousands of people from dying prematurely from heart attacks and strokes.
"We're therefore pleased to be able to recommend it as a cost effective option on the NHS."
Amanda Pritchard, chief executive of the NHS, said heart disease was still "one of the major killer conditions".
"It is fantastic that we now have such an effective and convenient treatment for those living with dangerously high cholesterol levels."
She said the rollout of inclisiran would save lives and benefit hundreds of thousands of people.