"The series for the Border-Gavaskar Trophy will now commence in Adelaide on the revised date of Tuesday 9 December," Cricket Australia said in a statement.
The second Test in Brisbane will start on December 17, followed by Melbourne on December 26 and the final match in Sydney, starting January 6.
A two-day tour game featuring a CA XI was cancelled last week, but India might get an opportunity to play a practice match later this week.
CA Chief Executive Officer James Sutherland thanked the BCCI for its continued support and understanding .
"The BCCI has shown great empathy and understanding which we truly appreciate. They have put the cricket community's concerns for the Hughes family well ahead of their own preparation," he said.
The revised schedule allows for a three-day break leading into the Brisbane Test and a four-day break ahead of the Boxing Day Test in Melbourne for players to adequately prepare.
"The Sydney Test has also been shifted as a result with its start date moving to January 6 to allow for six day break for players towards the end of a busy series," the statement said.
Sutherland said the changed program was made due to welfare concerns for Australia's players grieving the loss of Hughes who passed away last week.
Hughes' funeral will take place in his home town of Macksville on Wednesday. The entire Australian team, Indian cricket captain Virat Kohli, visiting side's coach Duncan Fletcher and Team Director Ravi Shastri will attend the funeral of the young batsman.
"Nobody should underestimate just what these players are going through right now. These are difficult days and we need to support them in dealing with their grief," Sutherland said.
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