The new schools - effectively state-funded private schools - will be introduced to South Auckland and Christchurch within the next three years.
NZEI president Ian Leckie said the Government had no mandate for charter schools.
"Overseas experience shows they can take students and money away from existing schools, undermine communities and increase social segregation. They are also less accountable.
"New Zealanders should be very concerned that Act is suddenly shaping and dictating key education policy."
Labour's education spokeswoman Sue Moroney called the trial "bulk-funding in drag" which exposed National's true colours.
Meanwhile, Act has also secured National's support in principle for a plan long promoted by Act founder Sir Roger Douglas, to limit growth in Government operating expenditure to take account of population growth and inflation.
The principle will be enshrined in a new law but there will be no penalty for breaching it except for the Finance Minister having to give an explanation to Parliament.
National's spending trajectory is well within the cap already, which is why it agreed to support something it has opposed in the past.
Mr Key has also agreed to annual monitoring by Treasury of certain indices between New Zealand and Australia such as income, productivity and "overall levels of economic freedom".
Yesterday he signed deals with Act MP John Banks and United Future leader Peter Dunne, giving National the numbers to lead a minority Government for a second term.
On provisional results, National has 60 seats in the 121-seat Parliament, requiring one more for a majority on confidence and supply issues.
If the Maori Party signs a support deal on confidence and supply, that will give National an extra cushion of three against problems that could arise to threaten stability. Mr Key remains confident the Maori Party will decide on another support deal rather than go into Opposition.
"They would be in a rather cluttered environment of Opposition with Labour, the Greens, New Zealand First and Mana. Frankly I find it impossible to believe that they would make more gains in Opposition than they would in Government with us."
The final election result is due to be declared on Saturday.
Mr Key said he would also try to get a decision from the Maori Party at the weekend, then go to the Governor-General and potentially swear in the Cabinet and other ministers on Monday or Tuesday.
The support party ministers will again be outside the Cabinet and will be given the right to criticise National Party policy outside the confines of National's action plan.
The proposed Maori Party deal would not require it to support National's action plan and would therefore give its ministers even more scope to criticise the Government.
Mr Dunne got National to agree to put into legislation its policy maintaining at least a 51 per cent state ownership of state-owned enterprises.
There will also be an investigation of a free annual health-check for over 65- year-olds "for implementation when fiscal circumstances allow".
What the junior partners got
ACT
* John Banks ministerial portfolios: Regulatory Reform, Small Business, Associate Education, Associate Commerce.
* Establish Charter Schools (free, state-funded, independently run) to take over under-performing schools or set up new ones.
* Pass law to set cap on government spending limits but with no penalty if breached.
* Annual reporting by Treasury on the income gap with Australia.
* Pass law to require better explanations of regulation-making powers in new legislation.
UNITED FUTURE
* Peter Dunne ministerial portfolios: Revenue, Associate Health, Associate Conservation.
* Law to prevent any sell-down of SOEs beyond 49 per cent.
* Cease helicopter hunting of game on conservation estates.
* Cut Families Commission commissioners to one and fund parenting courses and relationship education in schools with the savings.
* Discussion paper on "flexi-super" - different rates depending on age of uptake.
