The radical shift will be a key part of the Scottish Conservative manifesto and follows years of opposition to the Scottish Government policy pursued by SNP-led administrations.
Traditionally the Conservatives have objected to universal free prescriptions on the grounds that it costs the NHS too much.
With the latest figures suggesting the NHS in Scotland spends £2 billion per year on prescription drugs, the Conservatives have previously argued that those who can afford to pay should do so.
Over the last decade Scotland’s drugs bill has risen by almost 30 per cent and doctors’ organisations such as the BMA have called on the Scottish Government to ditch the policy on cost grounds.
The about-turn, which will be unveiled in Davidson’s manifesto this week, will be seen as an attempt by the Tories to rid themselves of their “nasty” party image.
Davidson’s opponents will portray it as the Tories trying to deflect attention from the controversy over UK government policies such as the two-child benefit cap and its associated rape clause.
Last year an Ipsos Mori poll found that the Conservatives’ existing policy to charge around £8 for prescriptions was one of the least popular policies of the 2016 Scottish Parliament election campaign, achieving an approval rating of just 5.3 out of 10.
Davidson will argue that increased access to prescription drugs will help keep patients out of hospital and enable them to be treated in primary and community care settings.
The Tories claim the emergence of increasingly sophisticated drugs, which can be customised to take into account a patient’s genetic make-up, is opening up more opportunities for patients to be treated outside hospital.
Davidson also wants to examine saving money by looking at the current use of “low-value prescriptions” such as over-the-counter drugs.
Statistics quoted by the Tories show the NHS is currently spending £10.5 million on paracetamol, £2.9m on aspirin, £1.6m on sun cream and £1.8m on shampoo.
The party will set up a new health advisory board to look at the policy as well as investigating whether an increased use of generic drugs and cutting down on drug wastage can save cash.
The new policy is also at odds with the Conservative party south of the border, where patients are charged for prescriptions.
Davidson argued for taking a different route to Theresa May’s government by saying: “That’s what devolved administrations and devolved parties do.
“We know there is a large amount of support for this policy. We think we can do prescribing better and we think this is sound,” she said.
With a Tory revival under way, Davidson also suggested that the policy was part of her attempt to transform herself from an opposition leader into a potential first minister.
“I have made no bones about the fact that my job when I was elected as leader in 2011 was to make the party fit to fight and to bring us forward,” she said.
“We showed from the increase in our vote from last year to this where people are looking at us and saying we quite like what you are doing in strong opposition.
“My challenge for the next four years is to turn us into a credible alternative government for Scotland, and this is part of it.”
The change of stance was described as “humiliating” by Scottish Labour, which, unlike the Tories, backed the SNP’s free prescription policy when it was passed by Holyrood in 2011.
At the time, the Conservatives argued the move was “politically irresponsible” and a drain on the public purse, pointing out that the young, the elderly and those on benefits were already exempt from paying.
Labour’s health spokesman Anas Sarwar said: “This is an embarrassing U-turn by the Tories. Ruth Davidson has shown once again she will do and say anything to try and get elected. All this humiliating shift shows is that once again the Tories simply can’t be trusted on the NHS.”
Former SNP leader Alex Salmond said: “The SNP’s flagship free prescriptions policy has been an overwhelming success and is one of the reasons that people continue to put their trust in the SNP after ten years in government.
“It’s the SNP that delivered free prescriptions, and it’s the SNP that will continue to deliver free prescriptions.
“Ruth Davidson used to describe free prescriptions as a ‘publicly funded bribe’, but this Damascene conversion shows that even the Tories can reluctantly recognise that it is the SNP that pursues the right policies for Scotland.
“While the Tories preside over a humanitarian crisis in the NHS in England, Scotland has the best-performing health service in the UK. If the Tories want to ditch their nasty party image, they should be U-turning on their indefensible, cruel policies such as the bedroom tax, the rape clause, cuts to housing benefits and the graduate tax.”
He added: “Now, more than ever, it is vital to have strong SNP voices standing up for Scotland. Only then can we protect Scotland’s schools, hospitals and pensions from unnecessary Tory cuts.”