Christian Brothers’ School and Loreto Grammar will propose the change to the Education Authority, with the aim of having no academic selection for year eight intake by September 2017.
Mr Lunn said it was good to see some schools “prepared to break the mould” and accept there was no need for transfer tests.
“Selection tests are unnecessary and divisive, and there is a need to continue to press for their complete end. Therefore this move by Christian Brothers’ School and Loreto Grammar has to be welcomed, as it will help remove some of the stress experienced by pupils during the school transfer process.
“We need to build consensus to find a fair solution that works for everyone. As it is, young people are being put under immense pressure, while avoidable divisions are being created with pupils from less disadvantaged backgrounds being given private tuition to help them pass the tests.
“I hope other schools look at the example being set and follow in the footsteps of these two schools, so we can help bring an end to the current unacceptable situation.”