The opening Test will take place in Brisbane on 11 June, with the second match in Melbourne a week later and the final game in Sydney on 25 June.
England, who beat the Wallabies 26-17 at Twickenham in November last year, have not toured Australia since 2010.
The teams, who first faced each other in 1909, will meet in Pool A of the World Cup on Saturday, 3 October.
Australian Rugby Union chief executive Bill Pulver said: "It is remarkable that Australia and England have never before played a three-match series and the history of this occasion is sure to add to the anticipation for the tour."
Australia will host England in a three-match series for the first time, after the 2015-16 Premiership season.