Young people will get a maximum of $50 a week in cash plus "incentive payments" of $10 a week if they attend education or training, another $10 if they attend budgeting classes and $10 for teen parents if they attend parenting classes.
Labour MP Jacinda Ardern said Labour wanted to impose the new system only as a "back-stop" if young people proved incompetent in managing their own money.
"Government members didn't wish to move to that regime, but instead have put in a provision that young people can earn their right to come off the [money management system]," she said.
The criteria for earning the right to manage your own money will be set out later.
Green MP Jan Logie said the Government had also agreed to clarify that teenagers could only be required to do "work-based learning" if this was paid at least the minimum wage.
"It has to be apprentice-type training, not work experience," she said.
Privacy Commissioner Marie Shroff urged the committee to delete sections allowing the Education and Social Development Ministries and private agencies to share information about young people, saying this should be left for a broader bill which is due back in the House on June 15.
The Government has kept information-sharing in the welfare bill so that it can come into force on July 30. But it has agreed to review the provisions in three years.
BENEFIT CONCESSIONS
* Teen beneficiaries will be able to earn the right to manage their own money.
* "Work-based learning" will have to be paid, not free work experience.
* Privacy provisions will be reviewed in three years.