Kallis was appointed their head coach in 2015, along with Katich as his assistant.
Kallis had earlier played for the franchise as well, and this decision brings his nine-year association with KKR to an end.
Speaking of KKR's performance under Kallis and Katich, they fared reasonably well.
Since October 2015, KKR made it to the IPL playoffs for three seasons till 2018.
However, that run came to an end this season, as they finished fifth.
Further, KKR also endured a six-match losing streak.
Meanwhile, Katich also led CPL side Trinbago Knight Riders to title success in 2017 and 2018.
"After nine fantastic years with KKR since 2011, as a player, mentor and Head Coach, it's time to explore new opportunities. I would to like to thank the owners, management and fellow players for many happy memories," said Kallis, after stepping down as KKR coach.
Commenting on the issue further, KKR CEO Venky Mysore said that Kallis still remains an integral part of the KKR family and could continue to work with them.
"We will be exploring ways of working with Jacques as we pursue our vision of establishing the Knight Riders brand as a global brand," said Mysore.
Even though Kallis has parted ways with KKR as the head coach, he is likely to continue with the franchise as a mentor. As for Katich, he is set to coach Manchester Originals in the upcoming and inaugural season of England's The Hundred.
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