The move continues a trend for residential colleges to move from church control to that of the University of Otago, though no decision has yet been made on who might take it over.
The college that helped produce the likes of All Black David Kirk, Health Minister David Clark and former prime minister Sir William English, as well as being the home of the Selwyn Ballet, has become difficult for the church to manage.
Selwyn College board of governors chairman the Rev Aaron Douglas said the problem for the church was "mostly one of capacity to manage the college, rather than a financial issue".
The church, and the University of Otago, have reassured prospective students this week the application process for placement at Selwyn remained on track for 2019.
"This has no impact on applications for 2019," Mr Douglas said.
The church is also considering a memorandum of understanding with an organisation, but would not say with whom.
Asked if the University of Otago was an obvious choice to take over the running of the college, Mr Douglas said the motion agreed to at the synod referenced the university as a party to any negotiations.
There would be "ongoing negotiations with the parties to the memorandum of understanding".
Dunedin Bishop the Rt Rev Dr Steven Benford released the motion agreed to by the synod.
The synod resolved to empower the Dunedin Diocesan Trust Board to sell the buildings and business of the college "to a party who is able to govern and manage the college".
That would be subject to a formal undertaking by the purchaser to "maintain the special character of the college".
The church would retain ownership of the land, entering into a lease agreement with any purchaser.
Dr Benford said there had been "robust discussion" over the last few years about the best way to support Selwyn College.
"The college has generally been well run and continues to be profitable, but concerns have been expressed from some members of the Selwyn board around the realities of managing and governing what is essentially one of the few remaining stand-alone residential tertiary colleges," Dr Benford said.
He said he realised Selwyn College had a strong profile in Dunedin and beyond.
"We will need to consider how best to engage with this wider community in looking at what the future may involve."
Asked if the church was concerned about losing its historic connection with the college, Dr Benford said it was "part of our DNA".
The nearby All Saints Church had a significant connection with the college.
"We don't want to lose this but want to explore ways to enhance it and make it even better."
A university spokeswoman said it would be "inappropriate for us to make comment", as it did not own the college.
