Clough, 26, most recently played for League Two club Carlisle United but previously also plied his trade in the English Championship and League One.
A Bolton Wanderers youth product, Clough made his senior debut for the club in 2015, scoring 22 goals in 68 matches across his first two-year stint there.
After leaving Bolton he signed for Nottingham Forrest before later returning to the Wanderers, while Clough also had stints at Rochdale and Wigan Athletic.
"I'm really excited about the opportunity to play in Australia," Clough said.
"I've heard great things about the A-League and I'm really looking forward to meeting my new teammates and getting to work.
"I'm a creative midfielder that loves to get forward and score goals and provide assists which will hopefully help contribute to team success."
Fourth-placed Adelaide have focused on bolstering their attack amid Ben Halloran's departure and Kusini Yengi's serious quad injury.
Clough, who can also play as a second striker, joins Japanese forward Hiroshi Ibusuki and on-loan youngster Lachlan Brook as recent Reds signings.
"Zach has great pedigree, playing at a strong level in England, and his signature gives us another attacking option," coach Carl Veart said.
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