Snedden is Director of the Ports of Auckland and has previously chaired both the Auckland and Counties Manukau DHBs.
He has received the NZ Order of Merit for services to education and Maori.
McGregor is head of the School of Social Sciences and Public Policy and Associate Dean Postgraduate in the Faculty of Culture and Society at Auckland University of Technology.
She is a former Human Rights Commissioner and is Patron of the Auckland Women's Centre.
Vui Mark Gosche is the CEO of VakaTautua, a national not-for-profit "by Pacific for Pacific" health support service provider and a former MP and Minister for Corrections, Housing, Transport and Pacific Island Affairs.
"No one should underestimate the task of governance in our public health service. DHB chairs play a vital role overseeing the delivery of health services to New Zealanders," Dr Clark said.
In a press release sent out on Sunday, Dr Clark also said he had decided to appoint a Crown Monitor at Counties Manukau DHB, which he said is dealing with a number of complex issues.
"The Crown Monitor, Ken Whelan, will attend and observe all CMDHB meetings and support the board as they continue to address these challenges," Dr Clark said.
Dr Clark said he wished to thank the acting chairs who have taken the reins at the three DHBs since December.
"Today's announcements represent a significant refresh of the leadership of Auckland's health services."