KKR team director Joy Bhattacharya on Tuesday said that Lee along with wicketkeeper Brad Haddin, pacer James Pattinson and Bangladeshi left-arm spinner Shakib-al-Hasan will be joining the team in Jaipur on the eve of their match.
The four players are currently busy doing national duties in the ongoing series between Australia and Bangladesh in Mirpur.
The series will conclude with the third ODI on April 13.
With their arrival, the team will boast of a full strength side ahead of their round three match.
The Kolkata outfit, who registered their maiden win of the season beating Deccan Chargers by nine runs last night, had a light practice in the afternoon today.
Opener Manvinder Bisla, Dutch all-rounder Ryan ten Doeschate and wicketkeeper Shreevats Goswami trained under coach Vijay Dahiya and his asistant Joydeep Mukherjee.
The team will leave for Jaipur tomorrow afternoon.