The Government pledge came after a Private Members Bill by Labour MP Geoffrey Robinson passed a significant hurdle in parliament with it second reading going through unopposed.
Health Minister Jackie Doyle-Price also confirmed that the Government would name the changes “Max’s Law” after Max Johnson, a 10-year-old boy who was saved by a heart transplant.
Ms Doyle-Price said: “We are supporting this Bill, we are determined to ensure that we secure more organs available for transplant, because we are very concerned that we are losing lives unnecessarily.
“At this stage it’s rather too early to draw any conclusions about the number of organs that the change in Wales has secured, but we have seen an increase in consent and opting on to the register.
“Our best estimates are that this change will secure an additional 100 donors a year, which could lead to the saving of 200 extra lives.
“On the basis that we could save 200 lives, we will wholeheartedly support this Bill.”
There was widespread praise for a national campaign to change the law, which put Max and his mother Emma at its heart.
“We in the Government will be referring to this as Max’s Law, and we will do everything we can to ensure its passage,” added Ms Doyle-Price.
At last year’s Conservative Party conference, Prime Minister Theresa May indicated that the Government would look to move to an opt-out system in organ donation.
MPs heard that around 1,000 people die every year while waiting for a transplant and England had some of the lowest rates of consent for organ donation in western Europe.
Mr Robinson said: “With any fair wind, shall we say, from the Government, by the end of the year we shall have put the Act, Max’s Act, as she called it, on the statute book.”
The Labour MP’s Organ Donation (Deemed Consent) Bill will now undergo detailed scrutiny by MPs at committee stage.
It must then clear further stages in the Commons and undergo scrutiny in the House of Lords before becoming law.
During the debate MPs heard that a grieving father’s decision to allow his nine-year-old daughter’s organs to be used to save four lives should serve as “inspiration” to others.
After Keira Ball died in a road accident last year, her father Joe made the decision to donate – saving the lives of a man, woman, boy and 10-year-old Max who had been in desperate need of a new heart.
Tory MP Peter Heaton-Jones, who represents Keira’s family, said the case demonstrated how “more organs means more saved lives”.
He said: “This could be an inspiration to ensure that they too sign up for organ donation and will give them strength if they have to face similar circumstances.
He added: “Keira’s story and Max’s story demonstrate that more organs mean more saved lives.
“I will be thinking of Max and Keira, it is their bill and it is thanks to the brave decision taken by Keira’s dad on that most difficult of days that four more people have life who otherwise might have not.
“That to me is the best argument for seeing this Bill reach the statute books.”