TDs backed the Dying with Dignity Bill by a margin of 10 votes, and it will now go to committee stage.
The government wanted a special committee to be set up to examine the bill - but that proposal was defeated.
Rise TD Paul Murphy sponsored the bill, and he says the outcome was very positive.
"A clear majority of the Dáil voted in favour of the bill in broad principal. So they support the idea that people with a terminal illness and in extreme pain can have assistance in dying.
"That does create real pressure on the Government now to allow this bill to progress to committee stage."
Right to chose
Right to Die Ireland said they were pleased that the Dying wIth Dignity Bill had passed to the next stage in the Dail.
In a statement they said "We have campaigned on this issue for the past eight years, since the deaths of Marie Fleming and Anne Holliday who we remember today.
"As well as lobbying politicians, we have made submissions to the Constitutional Convention and the Oireachtas Joint Justice Committee."
They thanked TD Gino Kenny for bringing forward the Bill and said we now need an "informed and compassionate debate that respectfully hears all concerns."
Meanwhile, Tom Curran, partner of Marie Fleming who campaigned for assisted suicide said:
“The Dying with Dignity bill was just passed to the next stage in the Dail. A true tribute to Marie Fleming and to all others who, unfortunately, this bill is too late to help.
"Ireland has come a long way to be a world leader in freedom and rights for its people and this in another step forward in giving the Irish people the right to choose.
"This bill, when it becomes law, will relieve the fear and anguish of the many people who are facing the probability of a painful and prolonged end of life journey. The Right to Die on our own terms is one of the last frontiers in a long battle to take control of our own beings, our bodies, our lives and our deaths."