Pujara, a veteran of over 100 Tests, was dropped following a poor run of form after the 35-year-old scored only 211 runs in his last six matches with one half-century to his name.
Jadeja claimed a career-best 7-42 as he and Ravichandran Ashwin (3-59) routed Australia for a paltry 113 in their second innings at the Arun Jaitley Stadium.
The 35-year-old will be the 13th Indian cricketer to play a century of Tests when he takes to the field against Australia in New Delhi.
India beat Bangladesh by three wickets in a nail-biting finish to the second Test in Dhaka on Sunday to take home the series 2-0. It was a hard-fought Test, which could have gone either way after a fairly one-sided first Test in Chattogram.
Cheteshwar Pujara emulated a feat of one of the most celebrated Indian batsmen of all time in scoring a double century for Sussex against Middlesex at Lord's on Wednesday.
Cheteshwar Pujara takes 54 balls to get off the mark during the third Test between South Africa and India.
Opener Murali Vijay and Cheteshwar Pujara hit sublime centuries to put India in command of the second Test against Sri Lanka on Saturday.
Cheteshwar Pujara and Ajinkya Rahane hit centuries as India take opening day honours on 344-3 at stumps against Sri Lanka in the second Test in Colombo today.
Virat Kohli strokes a commanding 12th Test century to put India in control at 302 for four when stumps were drawn on the opening day of the first Test against the West Indies.