The Mahendra Singh Dhoni-led side had already signed Hussey in the Chennai squad a couple of days back with the Aussie joining the team soon after as he was in India as an IPL commentator for the host broadcaster.
The 36-year-old, who has played 69 ODIs and 39 T20s for the Kangaroos, has plenty of IPL experience, having featured in 23 matches for Kolkata Knight Riders and 36 matches for Kings XI Punjab in previous seasons.
West Indies all-rounder Bravo was ruled out of the tournament after injuring his shoulder while fielding against Kings XI Punjab during the teams' first match in in the UAE.
There have quite a few injuries in this edition of the IPL with the technical committee approving all the requested replacements of the respective franchises.
Uttar Pradesh medium-pacer Praveen Kumar recently joined Mumbai Indians after Zaheer kHan bowed out with an injury while South African leg-spinner Imran Tahir was bought by Delhi as Nathan Coulter-Nile's replacement.