The Australians, who have lost their last nine series in India, also recalled all-rounders Mitchell Marsh and Glenn Maxwell to allow flexibility to deal whatever conditions they face in the four tests starting next month.
Top order batsman Shaun Marsh, Mitchell's brother, was also recalled after losing his place in the side for the series against South Africa and Pakistan through injury.
Jackson Bird was included in the 16-man squad as a third pace option along with Josh Hazlewood and Mitchell Starc, despite being dropped for the final test against Pakistan to allow two spinners to play in Sydney.
The Australians will review their fast-bowling resources after the second test in Bangalore.
"We don't know what pitch conditions we will come up against in each of the venues but wanted to make sure we have plenty of options available to us," head selector Trevor Hohns said.
"We know India is an incredibly tough place to tour and to succeed in, but we have a squad here which we believe can perform well enough in those conditions to give a good account of itself.
"No country has performed all that well over there in the last 10 years or more, but somehow, some way, someone has to turn the tide."
Leg spinner Swepson and left-arm orthodox spinner Agar, who played two tests in England in 2013, will act as back-up to off spinner Nathan Lyon and left-armer Steve O'Keefe.
Swepson, who has played 14 first class matches, won out over Adam Zampa because he is the more attacking of the two spinners, Hohns said.
"He is an exciting young leg spinner, he gives the ball a very good rip, he's a wicket-taking leg-spinner," he added.
"Given the opportunity, we think he could play a part over there. If he doesn't, he'll gain a lot from being there."
Hohns described Agar, who scored 98 with the bat on debut in the 2013 Ashes, as a "good all round package" who offered yet more versatility to the squad.
Mitchell Marsh edged out all-rounder Hilton Cartwright, who made his debut in the Pakistan series, because of his superior bowling, Hohns said.
Maxwell, a fast-scoring batsman who has been largely restricted to the shorter forms for his country, played the last of his three tests two years ago.
"Glenn is very experienced in Indian conditions, he's generally regarded as a good player of spin bowling, he's a good fielder and his off-spin is handy," said Hohns.
Opener Matt Renshaw and Peter Handscomb, who both impressed after making their debuts in the home summer, were also included, the latter offering back-up to the single specialist wicket-keeper, Matt Wade.
The first test starts in Pune on Feb. 23 and is followed by matches in Bangalore, Ranchi and Dharamsala.
Squad: Steve Smith (captain), David Warner, Matt Renshaw, Usman Khawaja, Shaun Marsh, Peter Handscomb, Mitchell Marsh, Glenn Maxwell, Matt Wade, Mitchell Starc, Josh Hazlewood, Jackson Bird, Nathan Lyon, Stephen O'Keefe, Ashton Agar, Mitchell Swepson.
(Editing by Peter Rutherford)
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