Lucknow had signed Pant for a tournament-record $3.21 million in the player auction before the 2025 season and put the wicketkeeper-batsman in charge of the squad.
They finished at the bottom of the 10-team league, winning just four of their 14 matches, prompting Pant to quit the captaincy.
Following the trade, the 28-year-old will rejoin Delhi, a franchise he spent nine seasons with including four as its captain, at a revised fee of $1.58 million.
Left-arm wrist-spinner Kuldeep spent five seasons with Delhi before his move to Lucknow.