India captain Virat Kohli and his wife, Bollywood actor Anushka Sharma, have announced the healthy arrival of their first child, a baby girl.

Kohli broke the news hours after the Indian cricket team fought back to hold Australia to a draw in the third Test of the series.

"We are thrilled to share with you that we have been blessed with a baby girl this afternoon," Kohli wrote on Twitter.

"Anushka and the baby are both healthy and we are feeling beyond blessed to start this new chapter of our lives.

“We hope that you can respect our privacy at this time. Love Virat.”

Indian cricket great Sachin Tendulkar was among those who congratulated the new parents.

"May her life be blessed with good health & love," he wrote on Twitter.

Adelaide Strikers’ leg-spinner Rashid Khan also shared his well wishes with the couple.

“Warmest congratulations to you and Anushka! Welcome to the club! Best wishes for the wonder-filled times ahead,” India’s number three Cheteshwar Pujara wrote.

Kohli returned to India on paternity leave after playing in the opening test in Adelaide, which his team lost by eight wickets.

However after levelling the series in the Boxing Day Test at the MCG, the team held for a gutsy draw in the third Test at the SCG, which finished yesterday.

Stand-in captain Ajinkya Rahane praised his depleted team for digging deep, highlighting the desperation showed by hobbled batsmen Hanuma Vihari and Ravi Ashwin as they successfully negotiated the entire final session.

“I’m really proud as a captain of each individual,” Rahane said.

“You don’t want your players to get injured but injuries are a thing you can’t control.

“Our talk in the middle and in the dressing room was if we need you to bat, you have to bat.

“Guys were ready for it. Credit to Hanuma, Ashwin was struggling, and (Ravindra) Jadeja was padded up.

“It shows their character ... it’s a very good sign.”

- with AAP