Finch, who was stand-in captain in Monday's One-day International against New Zealand, will take the helm for three matches in February, Cricket Australia announced Tuesday.
"It's very exciting to be back and leading the side in Steve's absence," said Finch, who has captained the national Twenty20 side on six previous occasions.
"It's been a rollercoaster from being captain leading up to the ICC World Twenty20 (in 2016), being injured and then Steve taking over the reins for that tournament, but it's something that any time you get the chance to captain your country in any format, you're very chuffed about."
"There are some extraordinary players around the country that will now get an opportunity and I think that's only a good thing for Australian cricket," he said.
Smith and Warner have been left out of the Twenty20 squad as they prepare for the four-test tour of India which begins on February 23.
Former opening batsman Justin Langer will step in as acting head coach for Darren Lehman for the Sri Lanka Twenty20 series which kicks off at the Melbourne Cricket Ground on February 17.
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