A Cliftonville statement on Friday evening said Lyttle had "tendered his resignation" and Sligo later confirmed his appointment to their vacant post.
Mal Donaghy and George McMullan will take charge of the Reds in Saturday's Premiership game against Glenavon.
Sligo sacked Dave Robertson earlier this month and Lyttle had been strongly liked with the job in recent days.
A Sligo statement said that Belfast man Lyttle, 39, had accepted a contract to the end of the 2018 season.
"Gerard joins us with a good track record from his time with Cliftonville," said Sligo chairman Martin Heraghty.
"He is ambitious and eager to bring success to Sligo Rovers. Gerard shares the vision we have for the club."
Rovers caretaker boss Declan McIntyre will remain in charge for Saturday's League of Ireland game against Derry City with Lyttle's first game at the helm next Friday's away game against Drogheda United.
The Reds have had a disappointing season but the timing of Lyttle's departure was a surprise with the club certain to be involved in a European play-off.
However, Sligo are only nine matches into their 33-game League of Ireland campaign and wanted to get a manager in place quickly after a poor start to the campaign left them second from bottom in the Premier Division table.
A Cliftonville statement said Lyttle informed club chairman Gerard Lawlor of his decision on Friday afternoon.
"Cliftonville FC wishes Gerard well in his future career," it added.
Lyttle was appointed in October 2015 following Tommy Breslin's departure.
The Belfast man did guide the Reds to last season's League Cup but Lyttle's attempt to put his own stamp on the first-team squad by letting a number of players go and bringing in others did not lead to the club earning any silverware this term.
In January, Lyttle did ensure that Joe Gormley will be returning to the club next season on a three-year deal after signing the striker on a pre-contract deal.
The Reds have had only one win in their last nine games and they are now 26 points behind leaders Crusaders.
Lyttle's final match in charge was Tuesday's 4-1 thumping by Ballymena United at the Showgrounds.
Gerard Lyttle has been appointed as the Sligo Rovers manager after resigning from his post as Cliftonville boss.