The council and the Anglican Diocese of Dunedin announced the move today.
SIT said the church would become part of the Creative Centre, between Tay St and Esk St, that is likely to cost up to $15 million.
SIT would fund the centre from its reserves, council chair Peter Heenan said. The purchase from the Anglican Diocese was approved at SIT's meeting on Monday.
The Creative Centre will include the church, a three-storey, 2250-metre-squared new building on the footprint of the church hall, an atrium joining the two and a cafe extension to the north of the church facing Esk St.
The demolition, strengthening and construction work would take place over the next two years with completion in time for the 2021 academic year.
SIT is delighted to be in a position to be able to purchase, strengthen, enhance and repurpose one of Invercargill’s icon historic CBD buildings, chief executive Penny Simmonds said.
While Ms Simmonds acknowledged it would be sad for the St John's parish to leave their much-loved church, SIT would be working closely with parish representatives to ensure the development enhanced and respected the church to give it longevity of use for the people of Southland.
The Anglican Bishop of Dunedin, the Rt Rev Steven Benford, said today it had been "a difficult process" for the parish and there is sadness at leaving a place that has been so important to them.
However, he believed the sale was a "positive outcome".
"They have increasingly been struggling to maintain this complex and the sale will enable the building - an important taonga (treasure) in Invercargill - to be preserved and used in new ways to the benefit of the wider community," he said.
"It will also free the parish to focus on its mission and ministry within Invercargill and beyond."
As well as teaching and exhibition space, the Creative Centre will also provide co-working areas for graduates and postgraduate students.
The vision for the Creative Centre is based on the Australian Centre for Moving Imagery (ACMI) in Melbourne.
SIT's programme manager for Creative Industries, Kathryn McCully, said that while the exhibitions and associated public programmes would be focused on moving imagery, technology and interactivity, the door was also open for other arts and creative practices to be part of the centre.
McCulloch Architects has been awarded the design work.
The project is important as a showcase for the creative industries at SIT but also as a contribution to the vibrancy of Southland's cultural offerings, Mr Heenan said.
The current SIT Downtown Campus would still be needed for the two-year duration of the Creative Centre build, and SIT was looking at options for the site from 2021, he said.