The programme has also been controversial. Education unions challenged the scheme in court after it was found to be breaking the law by placing graduates in positions that had not been advertised.
The programme was initially developed by the University of Auckland, but the partnership ended this year. It has been picked by The Mind Lab at Unitec, which is waiting on approval from the New Zealand Qualification Authority to run the programme.
Kaye said the $5.2m would come from within the tertiary education budget.
She also announced new initiatives in next week's Budget that aim to further lift the supply and quality of teaching.
There are about 100,000 teachers in New Zealand and Kaye said she had been advised that this was "a reasonable number to support our education system".
But she accepted there were pressures in some core subjects and some areas of the country.
As a result, the Government will give $2m to the Education Council to create an induction and mentoring programme that would allow teachers who were about to lose their certification to gain full registration.
About 6450 teachers have a provisional practising certificate. The new programme was expected to help 700 teachers who might otherwise leave the education system to get full registration, Kaye said.
Priority would be given to maths, technology and te reo Maori teachers and teachers in high-demand locations.
"By providing further support to teachers whose provisional certificate is nearing expiry we hope to encourage more of them to stay in the profession and gain their full certificate," Kaye said.
"Many of these will be relieving and part-time staff who are an essential part of the education workforce."
The Cabinet has also agreed to lift a moratorium on new teacher education programmes, beginning in January.
The moratorium was put in place in 2000 because of concerns about a proliferation of variable quality training programmes.
Kaye said quality assurance processes have since been strengthened.
Labour's education spokesman Chris Hipkins said National was "making up for lost time" after denying a teacher shortage for years.
The $5.2m boost for TeachNZ was ecliped by the $6.2m National had cut from the scheme, he said.
Hipkins said the Budget announcement did not address fundamental issues facing the profession, including the critical shortage of teachers in Auckland.
If in power, Labour wants to give teachers the right to elect their own professional body, raise entry criteria for teaching programme, and improve the quality of teacher training.