The England and Wales Cricket Board announced the change after Miller informed the governing body of his intention to step down during the summer's Ashes series. The ECB has also confirmed the appointment of former England wicketkeeper Paul Downton as their new managing director.
Former England all-rounder Miller, 61, took over from David Graveney as England's principal selector in January 2008. Since then, England have been ranked as the world's top side and won three successive Ashes series.
Ex-Leicestershire batsman Whitaker, 51, who played one Test in 1986, will take over in January, having been on the selection panel for the past five years.
ECB chief executive David Collier said: "Geoff Miller has been an exceptional national selector, presiding over selection during one of the most successful periods in England's cricket history.
"He developed an excellent relationship with the counties and with the England management team and he will be greatly missed by everyone at ECB.
"English cricket owes a great debt of gratitude to Geoff for the outstanding contribution he has made to the game and to the fortunes of our national team."
Meanwhile, James Anderson has signed a contract extension with Lancashire. The 31-year-old Burnley-born England bowler, who played a major role in the summer's Ashes success and will lead the tourists' attack in Australia, is now tied to Old Trafford until 2015.
"I am always proud to wear the Lancashire shirt and I am delighted to extend my stay," Anderson said.