The fast-bowling great had been in charge of the BBL's Strikers for nine summers, leading them to their first and only title in the summer of 2017/18.
Gillespie's side finished fourth on the ladder in the most recent campaign but were eliminated by eventual champions Brisbane Heat in a grand final qualifier.
Gillespie took the reins of the Redbacks in the summer of 2020/21, but the side finished in the bottom half of the Sheffield Shield ladder in all four of his seasons in charge.
Long touted as coaching material in the Australia set-up, Gillespie has been linked with the vacant Pakistan men's coaching role.
No formal announcement has yet been made by the Pakistan Cricket Board, who employed Mohammad Hafeez as interim coach for the tour of Australia last summer.
Gillespie will formally leave the South Australian Cricket Association in June.
"I am incredibly proud of what we achieved together at the SACA, and I will always cherish those memories," Gillespie said.
"I have no doubt that South Australian cricket has a bright future."Looking forward, I am excited to explore new opportunities in the sport and pursue the next chapter in my career."
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