The majority of the SKA dishes would be built in South Africa during phase one of the project.
Further dishes would then be added to an array in Australia, while low frequency aperture array antennas will be built in Australia and New Zealand during phase one and two.
Construction of the array would begin in 2016 and is expected to be completed in 2024.
The telescope would be made up of 3000 dishes, each 15 metres wide, with a complete surface area of one square kilometre.
It will be able to see into the universe 10 times further, and detect signals which are 10 times older.
It will also be capable of scanning the sky 10,000 times faster than any other telescope.
"This hugely important step for the project allows us to progress the design and prepare for the construction phase of the telescope," SKA Organisation interim director general Michiel van Haarlem said.
Science and Innovation Minister Steven Joyce said the announcement was a significant win for science and astronomy research in the country.
"The SKA presents an excellent opportunity for New Zealand science and business to benefit from involvement in a project of such international scale and significance," he said.
"Australia and New Zealand have worked hard, in partnership, to get to this point and we have established a solid foundation to continue our successful collaboration as we enter the next phase of the SKA project."
Sergei Gulyaev, head of AUT University's Institute for Radio Astronomy and Space Research, has said one of the tantalising prospects of the radio telescope would be its ability to give a "bird's-eye view" of the tectonic plates deep under New Zealand.
The Russian-born scientist said the radio telescope could use "quasars" - stable points on the edge of the universe - as a frame of reference for measuring the most minute changes on Earth.
"By observing quasars on the border of the universe, we create a fundamental reference frame in which we can study all the irregularities of the rotation of the Earth, ocean, tides, and solid earth, and the way an island like New Zealand is breathing."
Australian Science and Research Minister Chris Evans said sharing the project meant researchers would get the best results by capitalising on the infrastructure and strengths of both sites.
The Commonwealth and Western Australian governments had jointly invested more than $400 million in research infrastructure in previous research facilities, Mr Evans said.
"We have made a significant investment, delivered on our commitments, and we are continuing to develop technology that has the potential to further revolutionise radioastronomy."