Health Secretary Alex Neil announced the £21 million fund at the same time as the Scottish Medicines Consortium (SMC) decided not to recommend cystic fibrosis drug Kalydeco for use in the NHS.
The drug, also known as ivacaftor, was made available on the NHS in England at the start of the year.
As he announced details of the new fund, which will only cover the cost of medicines whose routine use has been rejected by the SMC, Mr Neil said: "It is only right that Scottish patients with rare conditions have access to innovative medicines which are clinically justified and that they are not disadvantaged due to the very high cost of these treatments.
"I am therefore pleased to confirm today that the Scottish Government will establish a fund which will ensure that the cost of successful new individual patient treatment requests for orphan medicines are met."
So-called orphan medicines are those that treat illnesses affecting fewer than one in every 2,000 people.
MSPs heard last year that the Individual Patient Treatment Requests (IPTR) system, which patients can use to get drugs not yet approved for general use by the SMC, is an "inequitable process" that favours young, middle-class and articulate applicants over more suitable vulnerable people who cannot speak up for themselves.
In November Mr Neil said a review would be carried out to look at current systems for making new medicines available across the NHS in Scotland.
A separate review is examining if the IPTR arrangements can be improved, with the new fund established after interim advice from Professor Charles Swainson - a former medical director at NHS Lothian who is now an independent consultant.
The £21 million is available from March through to April next year and will help cover the cost of successful requests under the IPTR system.
Mr Neil said: "This fund bridges the period to the establishment of next year's value-based pricing for medicines and any changes that are made following the completion of the ongoing access to new medicines review.
"We recognise that the Scottish Medicines Consortium is globally respected and has the fastest and most efficient medicine review process anywhere in the UK but that for some individual patients with rare conditions, there is a need for further support. This new fund will complement it by making the IPTR processes fairer."
Liberal Democrat health spokesman Jim Hume said the fund's creation shows that "all is not well with the current Individual Patient Treatment Request system".
He said: "While this extra money may help people access the medicines they need, ministers must make sure that the underlying problems around access to new drugs are tackled, so the system is fair for patients across Scotland regardless of background.
"I was deeply disturbed to hear evidence that articulate applicants are more likely to access medicines than vulnerable people who cannot speak up for themselves, or do not know the system."
The Cystic Fibrosis Trust has been campaigning for Kalydeco to be made available. The drug treats people who have the G551D cystic fibrosis mutation.
About 11% of people with cystic fibrosis in Scotland have this mutation, compared with about 4% in the UK, the charity said.
About 80 people in Scotland would have been eligible for treatment with Kalydeco, the trust estimates.
A spokesman for the SMC said it is aware that the decision not to recommend the drug for use in the NHS would "come as a disappointment".
He said: "Cystic fibrosis is a very difficult condition that has considerable impact on the day-to-day life of patients and their families. It is recognised that life is significantly shortened by this condition, with an average survival of 34 years."
Kalydeco is a "promising new medicine" but claims that it can increase life expectancy by as much as 18 years are "highly uncertain".
The spokesman said: "This weakness, combined with the very high cost of the medicine, were significant factors in the SMC decision. The cost of ivacaftor in NHS Scotland would be around £180,000 per year for each patient for life.
"The recent decision to make ivacaftor available in England is based on a discounted price that has not been offered to NHS Scotland. SMC is unable to comment further on the decision in England as, unlike SMC advice, the basis of their assessment has not been made publicly available.
"SMC aims to make decisions on the cost-effectiveness of new medicines in a way that is fair for all patients with all conditions and for the sake of patients with cystic fibrosis, we would welcome the opportunity to evaluate an improved case for this new medicine."
Ed Owen, chief executive of the Cystic Fibrosis Trust, welcomed the Scottish Government's decision to make "additional funding available to enable Kalydeco to be made available to those that need it".
He said: "We now appeal to Vertex, the manufacturers of Kalydeco, and the NHS in Scotland to work together to reach a fair and affordable solution as soon as possible.
"The CF Trust has campaigned for all people with the G551D mutation of cystic fibrosis who are eligible to receive Kalydeco to be able to receive it as soon as possible."
Tilda Black, whose seven-year-old daughter Maisie has cystic fibrosis, criticised the decision.
Her family is "absolutely devastated by the news that Kalydeco won't be licensed in Scotland...The people taking these decisions obviously have no idea what CF has done to sufferers' families. We can't understand why it has been blocked up here, despite it being prescribed in England."
Rutherglen MSP James Kelly, who has been working with the family, said: "This decision is a blow to cystic fibrosis sufferers who need Kalydeco to provide much-needed relief from their condition. It is unacceptable that the treatment is available in England but not in Scotland.
"It is time for Alex Neil to stand up be counted and intervene. The mutation is more prevalent in Scotland than England. It is described as the Celtic gene and yet people in Scotland will be denied access to a medication which could be quite literally life-saving.
"It is bizarre that healthcare in Scotland lags behind England in treating conditions that are more common here.
"I will be meeting Alex Neil later this week with Maisie's mum Tilda Black. I will be demanding that he intervene on behalf of those with cystic fibrosis who desperately need Kalydeco."