More than half of organs transplanted since a new system came into effect were from people whose consent was deemed.
Since December 2015, unless somebody in Wales registers to opt out, theirorgans are donated after they die.
Figures show that in six months to 31 May, a total of 60 organs were transplanted – 32 organs from people whose consent was deemed.
Of the 31 people donating organs, 10 were because of the new system.
The “landmark” system has saved dozens of lives since its implementation, cabinet secretary Vaughan Gething will tell assembly members on Tuesday.
Under what is known as soft opt out or deemed consent, people who are 18 or over, have lived in Wales for more than 12 months and die in Wales, will be regarded as having consented unless they register otherwise.
Of the 31 dead people whose organs were donated between December and May, 10 had not registered a decision to either opt in or out.
This figure compares to 23 people donating organs in the same period in 2014/15 and 21 in 2013/14, under the old system of people having to opt in before their organs were donated.
A Welsh Government survey also suggests the majority of the Welsh public is aware of the new law, with 74% of people able to describe changes to the system.
Mr Gething said: “The path to organ donation is a complex one, but consent is the stage at which most donations are lost.
“I am extremely proud that Wales now leads the way by being the first nation in the UK to move to a soft opt-out system of consent.”
He added that the law was introduced to address a “chronic shortage of organs for transplant” in Wales and “heart breaking stories” of people on donation waiting lists.
Mr Gething’s statement comes ahead of a new campaign aimed at getting more young people to talk about their organ donation decision and remind people of their options under the new system.