Adults in Wales will now automatically become organ donors after death unless they have registered to opt out.
The Welsh Government has changed the law regarding organ donation registration in order to help more people who desperately needing transplants in the country.
They estimate that the new system will increase the number of organ donors by as much as 25%.
According to the Press Association, only 8% of eligible adults in Wales have decided to opt out ahead of the new law coming into effect on Tuesday.
The latest figures show 14 people died last year in Wales while waiting for a transplant.
Wales' health minister Mark Drakeford said: "The change to a soft opt-out system for organ donation will deliver a revolution in consent.
"Organ donation saves lives; increasing the rate of organ donation allows us to save more lives. That’s the key motivation for this significant change."
Among those welcoming the new law in Wales is the British Heart Foundation (BHF) which says the rest of the country should follow suit.
BHF chief executive Simon Gillespie said organ donation rates in the UK are 40% lower compared with other countries in Europe that already use the opt-out system, such as Spain and Croatia.
"Sadly hundreds of people die every year waiting for a transplant because there is a desperate shortage of organ donors," he added.
"Other European countries that already use an opt-out system have much higher donor rates than the UK.
"We campaigned strongly in Wales to introduce soft opt out and now it’s time for the rest of the UK to follow their lead."
However, not everyone supports the new system.
Ahead of the new law coming into effect, the Press Association reported that several faith groups - including leading Welsh Christian, Jewish and Muslim clerics - signed an open letter expressing their unease about the plan.
The letter said: "We remain opposed to any weakening of the principle the donation of organs should be free and voluntary."
The Archbishop of Wales, Dr Barry Morgan, also reportedly expressed fears that the scheme could turn "volunteers into conscripts".
But in an open letter published on Monday, Church of Wales bishops said they are "wholeheartedly in favour of organ donation".
"It is love in action and a wonderful example of what it can mean to love our neighbours, especially those in need. Such generosity is a response to God’s generosity towards us," they added.
The bishops urged those outside of Wales to sign the Organ Donor Register.