The Bill recently passed a significant hurdle in the Scottish Parliament as MSPs agreed its general principles at Stage One.
It is aimed at overhauling the organ donation system in Scotland, by moving from opt-in to a soft opt-out mechanism, similar to the successful approach currently in place in Wales.
An opt-out transplant system means anyone over the age of 16 who has lived in Scotland for at least a year - and is considered capable of making an informed decision on the subject - would be considered to be a consenting donor, unless they have opted out.
There is broad consensus that the change would increase the number of organs available for transplant and ultimately save lives.
Mr Griffin has long supported a change and had proposed a Members’ Bill on this issue.
Following extensive discussions with the Scottish Government, Mr Griffin dropped his Bill, with the Scottish Government committing to move forward with plans.
As he announced his support Mr Griffin told his Parliamentary colleagues about his late father, former Kilsyth councillor Francis Griffin, who had to wait ten years for a new heart.
Unfortunately after finally receiving a transplant Francis did not recover as his liver, kidneys and other organs were not strong enough to cope with the operation.
He said: “I am delighted that the Scottish Government is taking action on this important matter and fully support the plans.
“Although 90 per cent of people in Scotland are in favour of organ donation, only 52 per cent are on the organ donor register. That has to change.
“Almost 12 years ago, my dad died shortly after receiving a heart transplant. He was 47-years-old. He had waited for a transplant for a decade and by the time it came his other organs were too weak to support him.
“My dad was lost to me and my family at such a young age, missing so many milestones in our lives. It is why I feel so passionately about this issue.
“I gave a commitment to withdraw my Members’ Bill if the Government took action and I am pleased they have. I am confident that the law will soon change and more lives will be saved.”
As it cleared Stage One, Dundee City West MSP Joe Fitzpatrick who repsented the Bill said: “I hope that the bill will lead to further increases in donation to save more lives, and I offer any such progress as a tribute to all those who have donated in the past.”