Lee, who has played in 35 Tests, proved his fitness during three matches for state side New South Wales and is the only change in the 12-man team named by the Australian selectors on Monday.
India lead the four-Test series 1-0 after winning the second Test in Adelaide by four wickets last week.
"Brett is an established Test player and has demonstrated that he is back to full fitness following injury," chairman of selectors Trevor Hohns said in a statement.
"Brett always adds some zest to the attack and will be supported by our other bowlers who we felt, despite the loss, served the side well in Adelaide."
Lee returns for the first time since the second-Test win against Zimbabwe in October.
DEPLETED STOCKS
Australia's depleted bowling stocks were reduced even further when injury-prone fast bowler Jason Gillespie broke down with a groin strain during the second Test against India and was ruled out of the traditional Boxing Day match in Melbourne.
Gillespie will travel to Melbourne with the side to continue treatment on the injury.
Fast bowler Brad Williams, a possible candidate for the 12th-man spot which will be announced later this week, has proved his fitness after injuring his shoulder in Adelaide. Left-arm paceman Nathan Bracken was 12th man in the second Test.
Strike bowler Glenn McGrath has been ruled out of the series while he recovers from ankle surgery. Leg spinner Shane Warne is also unavailable while he serves a 12-month doping ban.
But it was Australia's batting which drew most criticism from coach John Buchanan in Adelaide.
Buchanan described his side's performance as "soulless" and "immature" after they were bowled out for 196 in the second innings.
Australia team: Steve Waugh (captain), Justin Langer, Matthew Hayden, Ricky Ponting, Damien Martyn, Simon Katich, Adam Gilchrist, Andy Bichel, Brett Lee, Stuart MacGill, Brad Williams, Nathan Bracken (12th man to be named).
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