England's Livingstone joins Chennai for a fee of 60 million Indian rupees ($634,870), significantly less than the 130 million rupees Hyderabad paid to sign him, while Australia's Edwards moves at his existing fee of 30 million rupees.
In return, Hyderabad have brought back left-arm fast bowler Khaleel Ahmed, who returns after a previous stint between 2018 and 2021, and Australia pacer Ellis.
Khaleel will remain on his existing contract worth 48 million rupees, while Ellis joins for 20 million rupees.
Livingstone's arrival gives five-time champions Chennai additional firepower in the middle order, while Edwards will look to make his IPL debut after missing the entire 2026 season with a foot injury despite being signed by Hyderabad before earning his first Australia cap.
Khaleel made only five appearances in 2026 for Chennai before a quadriceps injury ended his campaign.
The deadline for franchises to submit their retention and release lists is November 17th, with the IPL mini-auction scheduled to be held in Goa on December 16th.