A new donor register will for the first time allow people to make clear if they do not want their organs used after their death.
Public Health Minister Maureen Watt said the change would provide a "more modern system which extends the choices people can make".
The new register, which was officially launched across the UK, allows people to sign up for their organs to be used after their death, but also lets them make their wishes known if they do not want to be a donor.
But Ms Watt stressed the importance of people making their wishes known to their families, pointing out that two-thirds of people who donated their organs over the last five years were not on the register.
A total of 41 per cent of Scots are registered as organ donors, the highest proportion of the population in the UK.
There are, however, about 540 people in Scotland who are currently waiting for a transplant operation.
Those who are already registered as organ donors will have their details transferred on to the new register by NHS Blood and Transplant.
Ms Watt said: "Whether you choose to be an organ donor or would like the NHS to know your decision not to be one, I would encourage everyone to take some time to think carefully about the important issue of organ donation and make your wishes known through the new register.
"However it is also vitally important that people make their wishes known to family and friends so that those wishes can be honoured in the event of a loved one's death."
She continued: "While joining the register is important, two-thirds of people who donated their organs in the last five years weren't on the NHS Organ Donor Register.
"Families who are aware of their loved one's organ donation wishes are twice as likely to say 'yes' to donating their organs.
"If you register without telling the people closest to you, it may come as a surprise to them. Knowing organ donation is what you would have wanted could make their decision a lot easier to live with at a time when they are trying to deal with their loss.
"Therefore the new register provides an ideal opportunity for people across Scotland to make sure their choices are up-to-date and to talk to family and friends about their decision to donate."
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