Clark, 66, served as prime minister on a government led by the centre-left Labour Party from 1999 to 2008 and has been the first woman administrator of the UN Development Programme since April 2009, Xinhua reported.
“Having served as the prime minister of New Zealand for nine years and held one of the top jobs in the UN for the past seven years, Helen Clark has the right mix of skills and experience for the job,” Key said in a statement.
“There are major global challenges facing the world today and the UN needs a proven leader who can be pragmatic and effective,” he said.
“Coming from New Zealand, Helen Clark is well placed to bridge divisions and get results. She is the best person for the job.”
Clark had a vast amount of experience in international affairs which would be hard for other candidates to match, said Key.
“She’s a great listener and communicator, and I know she will make a difference if elected.”
Clark said in a video statement on Twitter that she was honoured to be nominated to lead the UN.
“I’m running because I believe my style of leadership is needed and will help the UN face the serious challenges ahead,” she said.
Clark served three successive terms as New Zealand’s second woman prime minister.
She is generally thought to have maintained New Zealand’s independent foreign policy, notably resisting calls to join the US-led invasion of Iraq in 2003.
Clark was first elected to the New Zealand parliament in 1981 after a brief career as an academic specialising in political studies at the University of Auckland.
Current Labour Party leader Andrew Little has expressed his support for Clark.
“Renowned for her steely determination and formidable capabilities, she would make an excellent secretary-general,” Little said in a statement.
The new secretary-general will be appointed at the end of the year by the UN General Assembly on the recommendation of the UN Security Council.
New Zealand currently holds a temporary seat on the Security Council and the government claims it wants to make the organisation more transparent.
Current Secretary-General Ban Ki-moon ends his term in December and eight candidates have now been declared.
The job has traditionally been rotated around regional groupings, and Eastern Europe is seen as next in line.
New Zealand is in the Western Europe and Others group.