They succeed Margaret Collins, a former Clutha District Council appointee and board chairwoman, and Malcolm Farry, the former deputy chairman, in the biggest change in leadership of the board for more than a decade.
Several new appointees have recently joined the board, including University of Otago anthropologist Prof Glenn Summerhayes, who is a university appointee; Otago University Associate Prof Peter Dearden, an Otago Institute appointee; and Clutha council appointee Gaynor Finch.
Five long-serving board members have retired.
He also paid tribute to Mr Farry and the other retiring members for their significant contributions.
Mrs Collins has served as a Clutha appointee on the board for 21 years, including 12 years as chairwoman, starting in 1997, and resuming the role after two years as deputy chairwoman (2004-05).
Mr Crombie, who is a city council appointee, said the museum was a "fantastic" place and a "really successful" organisation.
Having joined the board only late last year, he was intent on listening and learning and wanted to facilitate to ensure all voices were heard around the board table, he said in an interview.
Although the museum faced difficult economic times, it had already built a track record of success, including its redevelopment and new-look atrium, and its tropical habitat attraction.
The museum had further hopes and plans and he aimed to help harness the "positive energies" at the institution and around the board table.
He praised the skills of fellow board members and was looking forward to the "totally different" perspectives they would bring.
Before yesterday's meeting, Mrs Collins paid tribute to the other retiring board members: Mr Farry, Richard Skinner, Prof Robert Hannah and Prof Lloyd Davis.
Mrs Collins lauded Mr Farry's dedication and support as deputy chairman and Mr Skinner's long and valuable association with the museum.
• Mr Skinner is the son of Dr H. D. Skinner, a former long-serving director of the museum (1937-52).
Mr Crombie is chief executive at Polson Higgs, business advisers, and is a former chairman of the Otago Polytechnic's governing council (2003-10).
A past president, in 2008, of the Institute of Chartered Accountants of New Zealand, he has also chaired the institute board since 2009, having also been elected for a three-year term late last year. He is also chairman of the joint Australia New Zealand Chartered Accountants board.
