Ms Parker is due to take up the position in 2015, the centre said in a press release Wednesday.
The National Centre of Indigenous Excellence provides innovative programs that give First Australians, particularly the youth, opportunities.
Ms Parker currently holds the position of co-chair of the National Congress of Australia’s First Peoples, which works to influence the Australian government on the policies that affect Indigenous Australians.
Ms Parker is also a director at Reconciliation Australia that is dedicated to breaking down barriers between Indigenous and other Australians, and co-chair of the Close the Gap campaign, which aims to achieve equality in life expectancy and health outcomes of Indigenous Australians.
She was previously editor of Indigenous publication Koori Mail.
In 2012, she was recognised for her dedication to Indigenous affairs when she was handed one of the the country’s "100 Women of Influence Awards" organised by the Australian Financial Review and Westpac.