Under the new arrangement, bridging visas will be issued to the asylum seekers as they await assessment for refugee status in Australia.
The move has been welcomed by the Australian Human Rights Commission, but concern remains over the wellbeing of the families as adult parents will not be eligible to find work.
"The Commission is concerned that the levels of financial assistance provided to people on bridging visas is inadequate to meet basic needs and children may be moved into difficult financial circumstances," a statement wrote.
Additionally, only children who arrived prior to July 19, 2013 will be released, with those being held on Nauru and Christmas Island also being excluded from the policy.
"It's important we get those who are in detention on the mainland out of detention," Mr Morrison told ABC Radio.
The announcement came days after Baptist Churches called on the Federal government to protect babies and children from the harmful effects of detention.
"We are convinced, on the basis of human rights and our moral obligation to asylum seekers, as followers of Jesus and as Australian citizens, that babies and children must not be placed in immigration detention either onshore or offshore," the Director of National Ministries for Australian Baptist Ministries, Reverend Keith Jobberns, said.
A report released last month by the Australian Churches Refugee Taskforce revealed the harmful psychological and physical effects of detention on children and adolescents.