Kohli will miss three Tests Down Under due to the birth of his first child.
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Kohli and his wife Anushka Sharma are expecting a child in January, and the Indian captain has been granted permission by the BCCI to return home after the Test series opener.
The battle for the prestigious Border-Gavaskar Trophy will kick-start with the pink-ball affair at the Adelaide Oval on December 17. Melbourne will host the second Test from December 26 while the third and fourth Tests will be played in Sydney Cricket Ground (January 7-11) and Brisbane's Gabba (January 15-19), respectively.
Kohli’s absence for the major part of the series is certainly a blow to broadcasters in the pandemic-affected year.
"I'm a little bit disappointed he's not going to be there -- and a bit surprised," Waugh told AFP.
"This was really shaping up as one the key series of his whole career after he's achieved just about everything. But obviously family comes first," he added.
Team India are due to leave this week for Australia, where they have to serve two weeks in quarantine before the first ODI on November 27.
Kohli will captain the visitors India in three ODIs, three T20Is and the first Test before heading home.
According to Waugh, Virat Kohli's absence "does take away from the series".
"It's a bit like a couple of years ago when India won without (David) Warner or (Steve) Smith in the side," he said. "You really want to win against the best possible opposition, particularly when this is like the heavyweight title fight."
Commenting on Kohli's decision, Cricket Australia interim chief executive Nick Hockley put a brave face and said "it was always on the cards".
"We're thrilled Virat is coming out for three ODIs, three T20s, the first-ever day-night Test against India, and we have to respect the fact he wants to be there for the birth of his first child," he told Sydney radio station SEN.
(With AFP inputs)