The Hove-based club announced the news on Monday morning, with the former Australian pace bowler to start work in January.
The 42-year-old is well acquainted with the English county game, having 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. He replaces Mark Davis who left the club last month.
“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 the Big Bash before taking up his new role.
“Having spoken with both Keith (Greenfield, Sussex’s director of cricket) and Rob (Andrew, Sussex Cricket chief executive), I know that there is some excitement around the capabilities of the current playing group.
“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.”
Gillespie was in charge at Yorkshire when they won a second straight Championship title in 2015, beating Sussex in the final game of the season to send them down.
Andrew believes Gillespie’s experience will help develop a side which finished fourth in the second tier last time out.
“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 a bit of stability and a coach of Jason’s experience to help mould a successful team over the next few years.”