Mr Costello, who was treasurer for more than 11 years in the Howard government (1996-2007), has been acting chairman of the fund since January 11 following the resignation of David Gonski to become chairman of ANZ Bank.
As treasurer he was responsible for the establishment of the Future Fund in 2006.
"Mr Costello's unique experiences and background at the most senior levels in government and in business will be a great asset to the Future Fund board," Treasurer Joe Hockey and Finance
Minister Mathias Cormann said in a joint statement on Tuesday.
The government has also appointed John Poynton to the fund's board of guardians.
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Mr Poynton will bring more than 40 years of experience in the financial services industry to the role.
He is chairman of Azure Capital and a director of Crown Perth, and previously served as a director of the Export Finance Insurance Corporation.
Mr Costello and Mr Poynton have been appointed to their respective positions for five years from February 4.
