Kewell joined Reds as head coach in May 2017 before leaving them for a manager's role at Notts County where he was sacked after just 14 games in charge.
In August 2020, he joined Oldham Athletic. The club are currently 16th in League One after a scoreless draw with Southend on Saturday.
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Kewell said on Twitter that he was proud of his players and coaching staff and was leaving "without any regrets".
The Australian was Oldham's seventh different boss since Abdallah Lemsagam became owner in 2018.
"I honestly felt we were making good progress despite the inconsistency at times," added Kewell, who won the Champions League as a player with Liverpool in 2005 and represented his country at two World Cups.
"I knew coming into this job that I wouldn't have a budget to work with and that time wouldn't be on my side".