Mr Mack, who stepped down as Morgan Stanley's chief executive at the start of January 2010, will be joined at the sovereign wealth fund by the former head of Hong Kong's central bank Joseph Yam.
The pair, who will serve two-year terms on the CIC advisory board, are to replace Arminio Fraga, chairman of Brazil's BM&FBovespa stock exchange, and Lawrence Lau, a prominent economist in Hong Kong who have both recently resigned, reports the Wall Street Journal.
Mr Mack's appointment will increase CIC's ties with Morgan Stanley after it purchased a minority stake in the US bank in 2007.
The advisory board's role is to provide guidance on issues such as corporate governance and investment policy.
Mr Mack was replaced in the chief executive officer's chair at Morgan Stanley by James Gorman, who worked as a co-president at the firm before his promotion.
By Asim Shah