A proposed timetable will see an opt-out organ donation Bill introduced into the National Assembly for Wales next year, with the new system implemented in 2015.
It would make Wales the first country in the UK to move away from the current "opt-in" organ donation system.
Under the proposals, anyone over the age of 18 who does not want to donate their organs posthumously would have to make their wishes clear.
But in certain circumstances, families would be able to challenge whether a relative's organs can be donated, for example if it is extremely distressing or if strong evidence is given that it is against the person's wishes.
The paper will now be subject to a three-month consultation until the end of January.
The Evening Times has launched a campaign to persuade the Scottish Government to adopt a similar system to address chronic shortages of organs and tissue for transplantation.
Three people die each day across the UK waiting for a transplant.
Research shows support for presumed consent is higher in Scotland than in England, Wales or Northern Ireland.
More than 23 MSPs have signed a motion supporting our Opt For Life campaign, which was lodged by SNP MSP Humza Yousaf at the Scottish Parliament earlier this month.
He said: "I congratulate Wales on taking this important step towards a more humane organ donation system.
"We know in the UK three people needlessly die every day from a lack of organs, it is a situation we desperately need to take action on and hopefully Scotland will learn from the journey Wales is undertaking.
"I know the Scottish Government has not ruled out looking into an opt-out system and I think it's time we moved the debate forward."
NHS Blood and Transplant (NHSBT) has said it will work within the framework of the proposed changes in Wales.
NHSBT will be involved in implementation of the new policy and will also consider the implications for the other nations of the UK whose consent system will not be changed by the new Welsh legislation.
Research shows most people in the UK would accept an organ if they needed a transplant, but only around 30% have joined the Organ Donor Register.