Alex Neil said a "comprehensive range of measures" would increase access to drugs as well as making the system more open to patients.
As part of that, the Scottish Medicines Consortium (SMC) - the body which approves new medicines for use by the NHS - has been ordered to look at how it can increase flexibility when considering what drugs can be prescribed to people with very rare conditions and terminal diseases.
This review is to be completed by the end of the year, with the aim of having new approaches in place early in 2014.
A special fund set up this year to cover the cost of medicines for individual patients with rare conditions, which are not available for routine prescription, is also being extended.
The Rare Medicines Drugs Fund had been due to finish in April next year but will now run until April 2016 - with up to £40 million being made available for this over the two years.
Investment of £1 million is being put in to make the work of the SMC more open and transparent.
Changes are also being made to the system for prescribing drugs that have not yet been approved by the SMC.
MSPs on Holyrood's Health Committee had complained the existing Individual Patient Treatment Request (IPTR) scheme made it hard for patients, particularly those with rare conditions, to prove they are suffering from exceptional circumstances which would merit them being given the treatment.
Now, the Scottish Government is proposing a peer approval system, which will be led by local consultants, for when a clinician wants to prescribe a drug that has not been approved by the SMC.
The changes are said to be the first step in a process setting up a Scottish model, where a value-based system is used when assessing new medicines for use by the NHS.
They were announced just after the SMC decided a new breast cancer drug will not routinely be made available to patients north of the border on the NHS, but a new treatment for lung cancer can be prescribed.
Scotland has become the first part of the the UK to approve crizotinib, which could be an alternative to chemotherapy for some lung cancer patients, for use on the NHS.
But at the same time the SMC ruled that a new breast cancer drug Perjeta will not be recommended for use, with manufacturer Roche branding that decision an ''injustice for patients in Scotland''.
Mr Neil today said it was "only right that Scottish patients have access to medicines that are clinically justified".
He said: "We have listened carefully to patients, charities and consultants, and put in place a comprehensive range of measures which will increase access to new medicines and make the system better and more open for patients.
"The SMC has a pivotal role in ensuring that new medicines are thoroughly assessed for clinical effectiveness.
"However the Scottish Parliament Health and Sport Committee recognised that the existing assessments are not always appropriate for medicines for use at end of life or for medicines to treat very rare diseases.
"So, I've directed the SMC to conclude a review by the end of the year to establish more flexible approaches in evaluating medicines for end-of-life care and treating very rare conditions to increase access to new medicines for Scottish patients.
"I want Scotland to be able to make medicines available which represent value to patients and these changes are the first step towards this."
As part of the shake-up, the SMC will be able to evaluate new medicines before they have been submitted for approval by drugs firms, if the treatments are thought to be clinically important for Scotland.
SMC chair Professor Angela Timoney said it shared the "Scottish Government's objective of increasing access to new medicines for patients in Scotland".
She added: "SMC fully supports patient access to clinically effective new medicines at a price that is fair for all.
"SMC are confident that we can play a key role in developing a future approach that truly reflects what people in Scotland value."
Cancer charities welcomed the changes, with James Jopling, Breakthrough Breast Cancer's director for Scotland, saying: "We are pleased the Scottish Government is recognising the vital importance of improving access to effective treatments at the end of life."
Mr Jopling said that women with secondary breast cancer - also known as metastatic breast cancer - currently only had "limited treatment options for what is an incurable form of the disease".
He added: "We urge the Scottish Medicines Consortium to come back with recommendations that put much-needed value on medicines which give people additional, good-quality months with their loved ones, which we know are invaluable to those with secondary breast cancer and other terminal conditions."
Eric Low, chief executive of Myeloma UK said: "I very much welcome the announcement from the Cabinet Secretary of a package of initiatives to improve access to new medicines in Scotland.
"I am very encouraged that the SMC will be given additional resources and a revised remit so that they can further build on and evolve their already excellent appraisal processes.
"It is critically important that while improvements to access to medicines are made we also ensure that we are getting genuine value for money, and that the pharmaceutical industry improves the type and quality of information it provides to get their medicines funded on the NHS. I strongly believe that the SMC are best-placed to help make this happen.
"Finally, and above all else, we need to make sure that all patients get access to the most clinically and cost-effective treatment and care."
Liberal Democrat health spokesman Jim Hume said the "long-awaited changes" being made would "do much to remove the veil of secrecy many often feel cloaks the drug approval system".
He added: "The decision to scrap the Individual Patient Treatment Request process should go some way to address concerns raised by a number of charities that often patients who shout the loudest or know most are most likely to gain."
But he also said that "clarity is needed on the new peer-approved process and what it will mean for patients".
The MSP stressed the need for a "two-pronged approach" to making new medicines available, as some drugs do not go on health boards' prescribing lists even after they have been approved by the SMC.
"A quarter of SMC-prescribed medicines do not make health boards' prescribing list," Mr Hume said.
"Unless access is improved in our hospitals and to the SMC, patients will still face real issues in having their case heard."
While he welcomed the review to approaches for prescribing drugs for those with rare conditions and terminal diseases, Mr Hume said this came after two reviews examining access to treatments.
Mr Hume said: "People will be understandably confused by the Health Secretary's latest review, which follows two separate reviews into the same issue last year. How many reviews does it take before the Health Secretary gets on with ensuring a fairer service for patients?"
Conservative health spokesman Jackson Carlaw said that while the changes would not give Scotland a cancer drugs fund - as the UK Government has established for patients in England - they did "appear to be a way of funding more drugs to treat cancer".
He said: "On that basis, we give this announcement a cautious welcome."
The Tory deputy leader added: "The key will be in the detail of the SMC's findings once its review is complete, but at least there is some positive intent here from the Scottish Government.
"This has been a long time in coming, and not having a cancer drugs fund has led to thousands of Scottish patients missing out on life-extending treatment their counterparts down south have benefited from.
"We've been campaigning on this for some time and I'm encouraged that some progress is finally being made."
Duncan McNeill, convener of Holyrood's Health and Sport Committee, said a report it published highlighted concerns about access to new medicines and called for a number of changes to be made.
He said it was "testament to the strength of parliamentary scrutiny" that "significant changes to the system" had been announced.
But Mr McNeill said MSPs would have to "await further detail on what the creation of the new peer approval system will mean for patients and if it will address the issues this committee has raised".
Mark Flannagan, chief executive of the charity Beating Bowel Cancer, said he expected the new peer review system for drugs not yet approved for routine use by the NHS would introduce "a presumption that a patient's clinician is the best judge of whether a particular treatment will work for them".
Mr Flannagan said the end of the IPTR system should "lift the barriers to doctors wanting to prescribe the latest cancer drugs they believe will benefit their patients".
But he added: "The real test will be whether doctors feel they have the freedom to prescribe, confident that any decisions are based on the interest of patients."
Drew Lindon, from Prostate Cancer UK, said while there was much to be welcomed "it remains unclear that enough is being done to put patients at the heart of the system".
He said: "In England, patients, patient interest groups and their nominated clinical specialists can give both oral and written evidence to inform drug appraisal meetings.
"After today's proposed reforms it remains unclear whether their Scottish counterparts will be afforded the same opportunities. What do people in England have to deserve these rights that people in Scotland don't?"
Meanwhile, the pharmaceutical industry welcomed the changes, with Andrew Powrie-Smith, director of the Association of the British Pharmaceutical Industry (ABPI) in Scotland, stating: "We welcome the Scottish Government's efforts to address the lack of access to new and innovative medicines for patients in Scotland."
He added: "Ultimately the success of the Scottish Government proposals will be judged on two things - do patients get access to new medicines and how quickly these are made available to patients."