Last December, Kewell, 38, told Australian media his coaching ambition was to manage Liverpool, who finished fourth in this season's Premiership to secure another tilt at the Champions League with Europe's top clubs.
"My ultimate goal is Liverpool ... You don't know unless you get thrown in there. I'm a big believer in sink or swim," he said at the time.
Crawley finished 19th in the fourth-tier of English football, five points clear of the relegation zone and winning one of their last 14 games.
"During his interview, Harry showed us great passion - that's need to make this team move onwards," Selim Gaygusuz, Crawley Town's director of football, said in a statement.
Kewell, who represented the Socceroos in the 2006 and 2010 World Cup finals, played for his country 56 times, scoring 17 goals. He also won the 2005 Champions League and an FA Cup during his five years at Liverpool.
He had been in charge of the Watford Under-23 side since June 2015 before leaving the club last month.
(Reporting by Hardik Vyas in Bengaluru; Editing by Alison Williams)
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