Dunedin Hospital is part of Southern DHB, which had its board members replaced with four commissioners in 2015 after a projected $42 million deficit.
Mr Blair said he was confident he would hit the ground running in Wellington but there was no quick fix.
"These organisations are like massive super-tankers and when they are on a course it takes a lot to change direction."
He said Health Minister Jonathan Coleman was keen for collaboration and co-operation between the adjoining DHBs.
"It is not an agenda of amalgamating DHBs at all, but extracting synergies where possible, Mr Blair said.
"Things like IT are obvious but there are other services. Already the Hutt provides plastic surgery services and Capital and Coast with its tertiary status provides high-end tertiary services for the whole region, including Hawke's Bay, MidCentral and others."
Mr Blair was appointed to the Hawke's Bay DHB for three years from 2013, sitting on its Risk & Audit Committee, and during that time was chairman of Cancer Control New Zealand.
Previous to that he was chief executive of Acurity Health Group (formerly Wakefield Health), bringing Wakefield and Bowen hospitals in Wellington together as one unit and Royston Hospital in Hastings.
He was general manager of Royston Hospital in Hastings from 1995 to 2007.
He will remain in Hawke's Bay despite the three out-of-town roles.
"I commuted for six years running a NZX-listed company in Wellington and it is quite manageable. With the use of technology nowadays where you live is less important. I'll spend whatever time I need in the Wellington region to get these jobs done but Hawke's Bay is my home."
Hawke's Bay DHB chairman Kevin Atkinson said he was disappointed to lose Mr Blair who has "an incredible amount of knowledge" in the health sector.
"My relationship with him started at when we developed a relationship for Royston to help with some of our public patients and that moved on to Wakefield."
He expected them to continue working together, saying Mr Blair's new positions would provide "enormous value" to Hawke's Bay DHB and help satisfy Health Ministry expectations of increasing collaboration between DHBs.
"We spend a large amount of money with patients in Wellington and we are looking at ways we can perhaps reduce the costs of that and have a more efficient service.
"Having Andrew there with his knowledge of the provincial issues we have had is going to be of enormous benefit to us moving forward.
He said Mr Blair had "quite a challenge" turning around two DHBs "but to be honest I can't think of anyone more qualified to do that".