The Judicial Appointments Commission Bill has passed second stage in the Dáil.
TDs voted 83 to 53 in favour of the Bill, which must now be examined by Oireachtas Justice Committee in September.
The Bill will establish a new body with a lay chairperson to select judges for appointment.
It has been criticised by some of the country's leading judges, but has been a key priority for the Independent Alliance Transport Minister Shane Ross.
It is likely the legislation will not be enacted until the Autumn.
Meanwhile, the chairs of three Oireachtas committees have been revealed.
There were three vacancies following the recent Cabinet reshuffle.
It is understood that the Fine Gael backbencher Josepha Madigan is to become the chair of the Oireachteas Budget Oversight Committee.
Her fellow backbencher Fergus O'Dowd is to chair the Transport, Tourism and Sport Committee, while Alan Farrell will chair the Children and Youth Affairs Committee.
