The centre, based at the university's college of human and health sciences, will offer osteopathy, post-bereavement care, midwifery support and brain injuries rehabilitation.
It is hoped the service will help ease the pressure on NHS services.
Students at the centre will observe and learn in a real clinical setting.
The centre, part of the £600m Arch project, a collaboration between the university and Abertawe Bro Morgannwg (ABMU) and Hywel Dda health boards to improve the way healthcare is delivered, is being opened by Health Secretary Vaughan Gething on Monday.
Academy directory Julia Pridmore said some of the services, like audiology and osteopathy, will be available for drop-in patients.
She added: "If we make it easier for people to have themselves checked out at the first sign of trouble, or even just to reassure themselves that they are healthy, then hopefully we can reduce the amount of cases which become acute, requiring costly and difficult hospital treatment later on."
The academy, together with bereavement charity Cruse, has created a children's bereavement support group.
One of the services currently in very short supply across Wales is specialist post-bereavement care for children and young people.
Dr Zac Maunder, who manages the group, said: "Research shows that early intervention can be enormously beneficial for bereaved young people, but all too often there are shortages of specially-trained counsellors and lengthy waiting lists.
"We now have the chance to provide a forum for young people to talk to us and each other."
The health secretary said the academy will "enable staff to engage in cutting edge research that will drive innovation and excellence in Wales".
A new academy dedicated to providing non-medical treatments will "transform healthcare" in south west Wales, Swansea University has said.