TDs voted in favour of the legislation by 90 votes to 15, with 12 abstentions.
It followed hours of debate and more than 60 amendments.
The Regulation of Termination of Pregnancy Bill will now proceed to the Seanad (Irish senate).
The Republic voted to overturn its abortion ban in a referendum in May.
Irish Health Minister Simon Harris said the passage of the legislation was a significant step forward in preparing for the introduction of termination of pregnancy services at the start of January.
The Regulation of Termination of Pregnancy Bill allows for abortion services to be provided "on demand" up to the 12th week of a pregnancy, in the case of a fatal foetal abnormality or where the physical or mental health of the mother is in danger.
Since the bill's introduction at first stage in October, there have been some minor changes, including a decision to review the legislation after three years, rather than five years as was originally planned.
Two different doctors will be allowed to assess a woman in early pregnancy and the offences section has been moved from the front of the bill.