The Human Tissue (Authorisation) (Scotland) Bill became law, with MSPs voting to move to a soft opt-out mechanism for organ donation.
In 2016, Mr Griffin sought to change the law by introducing a Members Bill, however committed to withdraw his proposals if the Scottish Government took action, which they now have.
Although 90 per cent of people in Scotland are in favour of organ donation, only 52 per cent are on the organ donor register.
The changes agreed will see Scotland move from an opt-in system, to soft opt-out, similar to the successful system currently in place in Wales.
Mr Griffin’s late father, former Kilsyth councillor Francis Griffin, 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.
Mr Griffin said: “I was incredibly proud to cast my vote on a matter that is very close to my heart.
“Too many families like mine have lost loved ones waiting on an organ. My dad died shortly after receiving a heart transplant. He was 47-years-old and had waited for a transplant for a decade. By the time it came, his other organs were too weak to support him. My dad was lost to our family, missed big birthdays, graduations, weddings and didn’t get to meet my daughters.
“I am delighted that the law has now been changed. It will increase the number of organs available for transplant and save lives. The Scottish Parliament has risen to the occasion and I am proud of the role I have played on this issue in recent years.”
Every household in the country will be contacted about the new law, and schools and communities engaged with in the coming weeks and months.