Regulations will set out the way in which attendance in an online learning environment will be measured.
The change is part of legislation that has been introduced by Education Minister Hekia Parata.
She said it was the biggest update to education in New Zealand in nearly 30 years.
"COOLs will be open to as wide a range of potential providers as possible to gain the greatest benefits for young people," Parata said.
"This innovative way of delivering education offers a digital option to engage students, grow their digital fluency, and connect them even more to 21st century opportunities.
"There will be a rigorous accreditation process alongside ongoing monitoring to ensure quality education is being provided."
Online schooling models are used overseas.
In the United States, there has been strong growth in the number of online charter schools, which are publicly-funded but privately-run.
Some of the schools in the US providing online tuition do not have physical classrooms - students and teachers work from home on computers, communicating over email or a web platform.
Charter or "partnership" schools were introduced to New Zealand as part of National's agreement with the Act Party.
A spokeswoman for Parata said the existing correspondence school Te Aho o Te Kura Pounamu would become an accredited online provider.
"COOLs are being opened up to as wide a range of potential providers as possible to get the greatest benefits for students. One of the advantages of more providers is the ability to develop specialist niche provisions, eg. in Asian languages."
NZEI president Louise Green said the experience of online schooling in the US was "woeful".
"All the evidence is clear that high-quality teaching is the single biggest influence in-school on children's achievement.
"Education is also about learning to work and play with other children and to experience both growing independence and a range of activities outside the home.
"This proposal was not subject to any consultation prior to appearing in the Bill. We are concerned it will open the door to a new market in private provision subsidised by the taxpayer that will take resourcing away from public schools."
Post Primary Teachers' Association (PPTA) president Angela Roberts said the change would only benefit private business.
"Our students are not a commodity to be traded on the open market...there is no new opportunity created by this. The only advantage is to business to dip their hand in to the public purse."
Labour's education spokesman Chris Hipkins said the move to online learning brought risks.
"Kids get a lot of social interaction at school, a lot of their personal development happens when they are at school."
NZ First education spokeswoman Tracey Martin said the changes amounted to a "social experiment".
"This continues to build on this governments belief that 'anyone can teach' and those that will pay the price for this ignorance will be out children."
Te Kura is currently the only correspondence school. The change would open it up to competition.
Act leader David Seymour, who is Under-Secretary to the Minister of Education, said the changes announced today were not about clearing the way for online charter schools.
That was because there was nothing in the current law that would stop a partnership school allowing students to learn online from home.
An application to establish an online partnership school was rejected by the Government-appointed authorisation board in 2013.
"In principle, partnership schools have offered this opportunity for a long time...who knows what future applications will come forward," Seymour said.
"I think the jury is still out about whether learning content online is a substitute for the social aspects of actually being part of a school community. But, look, it's quite possible for some kids that's exactly what they need."
Dame Karen Sewell, chair of the correspondence school's board of trustees, welcomed the changes.
"They will give young people and their whanau the right to choose the education that best suits their needs. Students could choose to learn online or face-to-face, or a mix of both, and have access to a much broader range of subjects regardless of the size and type of school they are attending.
"Many of these young people are referred to Te Kura after long periods of disengagement from education and when all other options have been exhausted," said Dame Karen.
"Under the proposed changes students, with the support of their whanau or school, could choose to come to Te Kura - or to another COOL - and continue with their learning programme in an environment which may be better suited to them."
Currently about 23,000 students use the correspondence school each year. About half of those students use Te Kura for subjects or curriculum adaptation which their own school does not provide.
A regulatory impact statement by Dr Andrea Schollmann, the ministry's deputy secretary of education system policy, said there was convergence between correspondence education and that done face-to-face.
"Evidence suggests that, where students have increased agency over their learning, including choice about where to enrol, this can increase their engagement...for some students, online learning may provide the best learning environment."
Another option considered was to let all students enrol in the correspondence school, but it was ultimately decided to open up the market by allowing any school, tertiary provider or body corporate to apply to become a COOL.
Dr Schollmann's impact statement did note that international evidence suggests access to online learning increased student movement between providers, which could harm learning. There is also a risk that schools could use the changes to "move on" troublesome students.
However, she noted that accreditation would be removed from providers who had poor results.
