Regular skipper and in-form batsman Aaron Finch was ruled out of the series-concluding tie on Sunday. Finch damaged his left hamstring during the 2nd T20I yesterday (January 29) in Melbourne. India won by 27 runs to take an unassailable 2-0 lead.
Left-hander Usman Khawaja has been named as Finch's replacement as the hosts aim to avoid 0-3 whitewash against the MS Dhoni-led side.
With Test and ODI leader Steve Smith and vice-captain David Warner both having left for New Zealand tour, the responsibility was handed to the experienced Watson.
"It is an honour to be asked to lead the side on Sunday, although the circumstances are far from ideal," the 34-year-old Watson said after his appointment on Saturday (January 30).
"We may have lost the series but there is a great deal to play for with the ICC World Twenty20 coming up and you can be sure we will be determined to do well in Sydney," he added.
Watson is Australia's second most experienced T20I player with 51 caps, only Warner (54) has appeared more often for Australia in the shortest form of the game. Watson will become the ninth player to captain Australia in T20Is.
He has previously captained his country in one Test and nine One-Day Internationals in 2012 and 2013.
It has been a big turnaround for Watson from being dropped from the ODI squad in the recently concluded series against India and now chosen as captain.
Australia squad: Shane Watson (captain), Cameron Bancroft, Scott Boland, Cameron Boyce, James Faulkner, Travis Head, Usman Khawaja, Nathan Lyon, Chris Lynn, Shaun Marsh, Glenn Maxwell, Shaun Tait, Andrew Tye.