Dame Judith Mayhew, who was elected on Tuesday, will join the board of directors on 1 March and take over the chairmanship from Sir Colin Southgate at the end of the current season in August.
Born and educated in New Zealand, Dame Judith is a barrister and solicitor and currently works as a special adviser to London mayor Ken Livingstone.
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"I am delighted to be able to be joining the organisation at such an exciting time
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Dame Judith Mayhew
"I have had a fantastic career in both the public and private sector and I am now looking forward to focusing my energies in a new direction with one of my favourite cultural institutions," said Dame Judith.
"The Royal Opera House has had a remarkable history and at present is enjoying an astonishing renaissance," she added.
"I am delighted to be able to be joining the organisation at such an exciting time."
"Fantastic job"
Dame Judith replaces the outgoing chairman - former EMI boss Sir Colin Southgate, who has held the position since January 1998.
The office can only be held for five years.
Sir Colin said the decision to appoint Dame Judith had been made on Monday after "an exhaustive selection process".
"I am sure she will do a fantastic job," he said.
During her early career Dame Judith taught law in New Zealand and at Southampton University, before taking up roles at the Sorbonne in Paris and at King's College in London.
Until last October she was chairman of the policy and resources committee at the City of London Corporation, effectively deciding the direction of the authority which runs the capital's financial district.
She remains a member of the City's police authority, and she is also a trustee of The Natural History Museum.