The change means people would be assumed to have consented to their organs being used to help others unless they had signed an opt-out.
The move would potentially increase the number of organ transplants that can take place in Scotland each year.
The Human Tissue (Authorisation) (Scotland) Bill contains safeguards to make sure people’s wishes regarding donation are followed and that families will be asked about their relative’s views to ensure donations don’t occur where the person would not have wished it.
The proposed new system also includes protection for adults without capacity to understand and adults residing in Scotland for less than 12 months.
Children under 16 will only be able to donate if they or someone on their behalf explicitly authorises it.
The Scottish Government announced plans for the new “soft opt-out” system last year after a public consultation revealed 82 per cent backing for the change.
Public health minister Aileen Campbell said: “We need to do all we can to further reduce the number of people in Scotland waiting for transplants.
“We have made significant progress over the past decade, and moving to an opt out system will be part of driving a long term change in attitudes towards organ and tissue donation.
“Organ and tissue donation is an incredible gift. Importantly, under the proposed system, people will still be able to make a choice about donation as they can now and there are safeguards to ensure their wishes are followed.
“I would encourage people to continue to make a decision about donation and to tell their family.
“Organ donation can only occur in tragic circumstances, and every donor, supported by their family, makes a selfless decision that can save other people’s lives.”