"It's still really important for all of us to have conversations with our loved ones about organ donation so our wishes can be met if the worst should happen".
Legislation to introduce the new framework will be debated in Parliament later this year, the health department said on Sunday.
The new scheme will also include an opt out for those who do not wish to take part.
The change has been named Max's Law after 10-year-old Max Johnson, who was saved by a heart transplant.
But Mr Beggs warned that unless it is also extended here, Northern Ireland will soon be the only part of the United Kingdom without an opt-out system.
Guo Yanhong, an official with the National Health Commission, said in July that China was expected to become the country with the most organ donors by 2020.
The figures show 23 people became lifesaving deceased organ donors over the a year ago, helping the United Kingdom reach its highest ever number of donors.
"Tragically, that means people are continuing to pass away each and every year in Northern Ireland whilst waiting for a transplant".
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'We believe that by making these changes, we can save as many as 700 more lives every year.
A similar opt-out system has been in place in Wales since 2015.
However many over 50s don't join the NHS Organ Donor Register or tell their families they want to donate because they don't think their organs could help other people.
Research found that 82% of people in England support organ donation, but only 37% have indicated so on the register. I want to encourage people who wish to give life in the event of their death to take the time to record their wishes and discuss it with their family.
A courageous caller who lost her husband to liver failure perfectly explains why a new opt-out system for organ donations is so important.
Doyle-Price added: "We know this new system alone is not a magic bullet".
In the United Kingdom in 2017, 411 people died before the right donor was found, and more than 5,000 people are now on the waiting list in England.
"It can not be right that a shortage of donors means people from minority ethnic backgrounds wait longer for a transplant than others", Jackie Doyle-Price, Parliamentary Under Secretary of State for Mental Health and Inequalities, said.