The 30-year-old is on standby after Marsh pulled up sore following their 295-run thrashing by the visitors in the first Test at Perth on Monday.
Webster has been in red-hot form for Tasmania in the domestic Sheffield Shield over the past 18 months, with his seam-bowling prowess and explosive batting catching the eye of selectors.
“[Beau] Webster will join the squad next week having been named the Sheffield Shield player of the year last summer and continuing that form this season,” Cricket Australia (CA) said.
While questions remain around the fitness of Mitchell Marsh Marsh, Australia coach Andrew McDonald has indicated they will likely stick with the same team despite being outsmarted in Perth.
Webster and the rest of the squad are set to arrive in Adelaide earlier than anticipated to get in extra training sessions ahead of the day-night Test starting on December 6.
After Adelaide, the series moves to Brisbane for the third Test, which is scheduled to be played from December 14 to December 18.
The iconic Melbourne Cricket Ground (MCG) will host the fourth match from December 26, while the final Test will be played in Sydney from January 3.
Australia squad for the second India Test
Pat Cummins (c), Scott Boland, Alex Carey (WK), Josh Hazlewood, Travis Head, Josh Inglis, Usman Khawaja, Marnus Labuschagne, Nathan Lyon, Mitch Marsh, Nathan McSweeney, Steve Smith, Mitchell Starc, and Beau Webster.
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