The 42-year-old led Yorkshire to promotion from the second division in 2012 and back-to-back titles in 2014 and 2015.
He ran Trevor Bayliss close when he was appointed as England coach and earlier this year had a short-term spell with Kent.
"I am thrilled to be given the opportunity of taking the reins at such a proud and traditional club like Sussex," said Gillespie, who will coach the Adelaide Strikers in Australia's Big Bash before taking up his new role.
"I look forward to getting over there and playing my role in helping Sussex achieve its on and off-field goals for 2018 and beyond," he added.
"Jason is exactly the experienced head coach we had hoped we would attract to the role," he said.
"He has enormous experience of the English county game after his very successful spell with Yorkshire.
"We believe we have a very talented young squad and we need a bit of stability and a coach of Jason's experience to help mould a successful team over the next few years.
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