SDHB commissioner Kathy Grant, who succeeded Mr Crombie in chairing the Otago Polytechnic council and sat on the board of Dunedin City Holdings with him, was influential in his appointment as deputy commissioner, alongside fellow deputy Richard Thompson.
"The three of us worked as a team," Mrs Grant said.
"I feel in many respects that I have lost my left hand or my right hand.
"Graham was one of my reference points, as Richard continues to be."
Mrs Grant sent a message to all SDHB staff last night, which said Mr Crombie died after having undergone complex surgery.
"I want to acknowledge with gratitude the efforts and compassion of our staff towards Graham while he has been in our care.
"Graham was an exceptional individual who made a phenomenal contribution to Dunedin and beyond, and I have no doubt that tributes will flow from many quarters as our community tries to process this news."
While Mr Crombie's accountancy expertise had been a leading reason for his appointment as deputy commissioner, his contribution to the organisation was far wider, Mrs Grant said.
He was chairman of the board's Southern Future Advisory Group, and also steered the South Island Health Alliance's information systems committee's work on integration of health information across the wider South Island.
Mr Crombie was 55.
