Fast bowler Tait was recalled to the 12-man squad after missing last month's series against Sri Lanka with injury.
All-rounder Hogg replaces leg-spinner Stuart MacGill, who has been ruled out after undergoing wrist surgery.
"Brad deserves the opportunity to once again represent Australia," said chairman of selectors Andrew Hilditch.
"He replaces MacGill in the squad, based on his Pura Cup performances to date and his consistent performance for the one-day international team."
Tait was originally selected for the series against Sri Lanka, which Australia won 2-0, but missed out after injuring his elbow.
His place was taken by Ben Hilfenhaus, who did not play in either Test, but was included for the India contest after proving his fitness.