Glasgow MSP Drew Smith said he was proposing a Member's Bill modelled on the document submitted to the Welsh Assembly which will introduce a system of presumed consent in 2015.
Mr Smith said the "simple change" to a soft opt-out system, with safeguards, would save lives and that it was essential that the wheels were now "set in motion".
He was among the MSPs who spoke at a debate yesterday at the Scottish Parliament calling for a switch to an opt-out system, which was overwhelmingly backed by members.
The Evening Times was praised for getting the public debate underway with our award-winning Opt for Life campaign, which has been backed by more than 10,000 readers.
SNP MSP Kenneth Gibson said the Scottish Government had to stop chasing the "Holy Grail" of enhanced registration to the current system, which has failed to dramatically increase the number of donors.
Mr Smith said: "In order to get a registration system in place that addresses any concerns we have to get the wheels in motion now.
"It is a change that would save lives and it is a change that is within our gift.
"The process needs to begin as soon as possible. There is a significant level of support.
"Those who wish to donate could have greater confidence that their wishes would be respected, and we know from research that countries which have opt-out systems in place have higher donation rates."
Mr Smith said he had already met with the British Medical Association to push his plans and will be writing to the Scottish Government to outline his proposal.
The debate was prompted by a motion raised by Mr Gibson, SNP MSP for Cunninghame North, which calls for a change to an opt-out system, which was supported by 43 MSPs.
Previous research by the Evening Times has indicated more than half of MSPs are in favour such a change.
Mr Gibson said: "As a result of organ shortages 43 people tragically died last year.
"I believe Parliament must tackle this problem now.
"The soft opt-out system would save dozens of lives every year."
Patricia Ferguson, Labour MSP for Maryhill and Springburn, said: "People in Scotland are dying unecessarily because some of us just haven't got round to signing the organ donor register.
"We've come a long way but it's now time to go further and to adopt the kind of scheme that has increased organ donation in other countries by between 25 and 30%.
"If we achieved this we would take 195 people off the transplant list."
Dennis Robertson, SNP MSP, spoke out following the death of his daughter Caroline, 21 months ago, from an eating disorder, who had said from an early age she wanted to be a donor.
He described the administrative process of consent that he had to go through to agree to donate his daughter's corneas.
He said: "It is a process which I believe ensures that organ donation is only carried out with those who have consented.
"Having presumed consent, which I fully support, has the soft option there, it has the safeguard.
"I hope that one day we can support a legislative programme."
Former health minister Malcolm Chisholm, Labour MSP for Edinburgh North and Leith, said he was "open-minded" about opt-out and praised the Belgian system which has both an opt-out and opt-in register.
The country has the second highest donation rate in Europe.
Glasgow Labour MSP Anne McTaggart, said: "It's clear that we have an organ donation crisis in Scotland and tough decisions need to be made to rectify this."
Other MSPs who spoke out in favour of change included Jamie Hepburn, SNP MSP for Cumbernauld and Kilsyth, Mark Griffin Labour MSP for Central Scotland and Liam McArthur MSP for Orkney.
Only two MSPs opposed to a change in thse system – Jackson Carlaw, Tory MSP for West Scotland, and SNP MSP Christine Grahame.
Closing the debate, public Health Minister Michael Matheson reiterated the Scottish Government's stance that opt-out is "not off the table" and said it was waiting for the organ donation taskforce's 5-year review which is due to come to an end in early 2013.
Mr Matheson said the government would also be monitoring the situation in Wales, which is due to implement a system of presumed consent in 2015.