There were 24 heart transplants north of the Border last year, compared to eight in 2012.
At the same time, 113 people joined the Organ Donation Register, representing a 31% increase from the previous year.
Professor Peter Weissberg, medical director with the British Heart foundation, said: "It's fair to say that the increase in heart transplants is due to the greater number of organ donors in the country.
"The limiting rate to performing transplants anywhere in the United Kingdom is the availability of organs, so naturally the work being done to increase organ donation has been key.
"Attention should also be drawn to the use of Ventricular Assist Devices at the Golden Jubilee. These mechanical hearts are crucial in keeping patients alive long enough for them to receive a viable donor."
The rise in heart transplants has been welcomed by patient care groups in Scotland
Dr Jean Turner, executive director of Scotland's Patient Association, said: "Having more opportunities for patients to receive a donor heart is excellent news and it is great that more and more people are having successful transplants.
"Our dedicated heart transplant unit at the Jubilee is now becoming well-known as a specialist centre which will help us to provide better care to those in need of a new organ.
She also welcomed the news that more people were coming forward to become donors.
She said: "It is always such a waste when someone dies and the person's organs are not put to use when they could have given another person life.
"Families should always talk to each other about organ donation. It's not something that should be left until after someone has died, leaving the relatives with a decision like that."
The majority of lung and heart transplants are carried out by the Scottish National Advanced Heart Failure Service based at the Golden Jubilee National Hospital in Clydebank, near Glasgow.
Mark Petrie, director of the service, said: "The aims of our strategy were to develop a consistent, equitable, Scotland-wide referral pathway for advanced heart failure.
"Since 2007, the number of organ donors in Scotland has significantly increased, which is fantastic as it has allowed us to help more people than ever before. However, moving forward, there is a need to have a further increase in this number to ensure we meet the need of everyone requiring heart transplantation."
The public health minister Michael Matheson added: "Our work on organ donation and transplantation continues to go from strength to strength and so it's great to see record levels of people receiving the life-saving transplant that they desperately need.
"Of course none of this would be possible without the generosity and thoughtfulness of those who have donated their organs and, in doing so, saved the lives of others."