Some schools are planning two-storey blocks to preserve threatened playing fields, and inner-city Newmarket Primary will rise to three storeys.
The biggest building projects are in central Auckland where 14 schools will get more than 100 new and replacement classrooms.
And 13 South Auckland schools, 11 on the North Shore and in West Auckland and three in the east of the city will also benefit.
Kaye said the new classrooms would be ready by the start of 2017.
Today's announcement marks the first tranche of the Government's accelerated Auckland growth package, and Kaye said the Government was committing $350 million in spending over the next four years.
The new classrooms would be ready by the start of 2017.
"We've given the green light to more than half of classrooms that we expected to be built over a number of years," she said.
The state-of-the-art classrooms will be "innovative learning environments", with heating, lighting, ventilation and acoustics supporting a range of learning approaches.
"It is important parents have confidence their local school will be able to accommodate their children," said Kaye.
The city's primary principals said in many cases the new buildings would be "in the nick of time".
"We would hope we are able to make a good dent in replacing classrooms so that all students have safe and healthy working environments and that [the classes] arrive in a timely way so schools can cope with the expansion of the network in Auckland," Auckland Primary Principals' president Frances Nelson said.
Mt Albert Grammar headmaster Dale Burden said the additional classrooms would help accommodate an "exponential increase" in in-zone students.
"The big pressure is coming. We know the spurt is coming through because of what the primaries and intermediates in central Auckland are going through currently."
He said the new block at his school would house its science department and would be designed to add a third storey for future roll growth.
"We are adamant we're not going on to our fields because we like our kids having green space so we've future-proofed everything," he said.
St Thomas's School principal Michael Maher said the prospect of 11 new classrooms was exciting as the roll tipped a record 830 pupils, a 130 rise over the past three years.
"It will support the school to continue to implement modern learning practices and provide our students and staff with a 'fit for purpose' learning environment."