The revolutionary system means adults automatically become donors after their death - unless they have chosen to opt out beforehand.
The Welsh Government predicts the new law could increase the number of organ donors by as much as a quarter.
In a statement bishops said organ donation was a "wonderful example of what it can mean to love our neighbours".
They said: "Whatever your views about the principles of Act, the fact remains that there is a great shortage of organs for transplant.
"220 people are currently on the waiting list in Wales - and one donor can save several lives. In 2014-15, 73 deceased donors supported 173 life-saving operations; but sadly, 12 people died whilst waiting for a transplant.
"As Bishops we 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.
"We urge and encourage you to sign the Organ Donor Register, and tell your families, so that there can be no doubt about your wishes in the event of your death."
But previously the Archbishop of Wales, Dr Barry Morgan, expressed fears that the scheme could turn "volunteers into conscripts".
Several faith groups - including leading Welsh Christian, Jewish and Muslim clerics - signed an open letter expressing their unease about the plan.
It said: "We remain opposed to any weakening of the principle the donation of organs should be free and voluntary."
Under the new system, those over 18 will become potential donors either by registering their decision to opt in - as they do currently - or by doing nothing at all.
It will apply to adults who have lived in the country for more than 12 months.
Organs available will be the same as the "opt-in" method - including kidneys, heart, liver, lungs and pancreas - and would go anywhere in the UK.
Listen to Premier's Hannah Tooley speak to the Bishop of Swansea, Revd John Davies here: