He was India captain Rohit Sharma's opening partner in the home T20 series against Afghanistan earlier this year but his place looked under threat as he struggled for runs in the IPL
"The BCCI has granted paternity leave to the Indian captain. He will return after the first Test against Australia in Adelaide," board secretary Jay Shah said in a statement.
India will leave for Australia late this month to play six short-form internationals followed by a four-test series.
Kohli's actress wife Anushka Sharma is pregnant with their first child.
Kohli's deputy Ajinkya Rahane will lead India in the final three tests.
India also added Rohit Sharma to their Test squad for the Border-Gavaskar Trophy after initially not naming him in the touring party because of a hamstring niggle.