Labor has vowed to fix the "unfairness" in the Turnbull government's schools funding plan, as the prime minister hailed it as the biggest-ever reform in education.
The early-morning parliamentary win was an outstanding result for schools, students, their parents and teachers, the prime minister said.
"Now that we've got the funding model right, the next step is to make sure we get the great educational outcomes," Mr Turnbull told reporters in Canberra on Friday.
That's down to businessman David Gonski, the original model's architect, who will conduct a further review.
Mr Turnbull later visited Santa Sabina College in Sydney which is due to receive an estimated $19 million extra over a decade.
Labor leader Bill Shorten, who with deputy leader Tanya Plibersek visited Holy Trinity primary school in Canberra on Friday, gave a simple commitment.
"If the Turnbull government does not fix the unfairness in its school funding cuts at the next election, we will," he said.
The suburban primary school is expected to lose just under $300,000 over a decade under the new funding model.
"This is a funding system that entrenches underfunding for public schools, for low-fee Catholic schools, and continues to give very substantial increases to some of the wealthiest schools in the country," Ms Plibersek said.
Labor's scheme would ensure "the largest increases in the shortest time go to the neediest schools", she said.
The opposition education spokeswoman also questioned the new school resourcing board which she said would comprise "a hand-picked panel" answering to the minister.
The new school board will review the schooling resource standard, which is the basis of the new needs-based funding model, and a guarantee the states won't withdraw their funding as more federal money flows through.
The reviews can address whether the commonwealth, states, territories or authorities are not distributing funding on a needs basis, or whether schools are being over or underfunded.
Education Minister Simon Birmingham, who guided legislation through the Senate and garnered the support of 10 crossbenchers, said all stakeholders could now have confidence in the funding model.
"We put the bucks in place, how do we get the best bang for our bucks?" Senator Birmingham told reporters.
"We expect the states and territories to work with us, agreeing to reforms that lift the quality of our teachers ... and access the best products and programs to use in their classroom."
The coalition won crossbench support for the reforms by shovelling an extra $5 billion into the plan, boosting it to $23.5 billion over the next decade.
The Gonski 2.0 package will ensure underfunded schools reach funding targets in six years instead of 10 and $50 million will be spent on a transition fund for Catholic and independent schools over 12 months.
ACT Catholic education director Ross Fox said the transition fund would mean no child who enrols in a Catholic school in 2018 will face pressure on fees or funding cuts.
However he said the legislation does not fix the long-term problems in the funding model for Catholic schools.
"Catholic education will continue to work with families and school communities to achieve fair funding for all schools and students."