Moores' departure had been widely predicted after England failed to get out of its group in the Cricket World Cup and then drew 1-1 in a test series in the West Indies.
The England and Wales Cricket Board says in a statement that Moores left his job following talks with Strauss and ECB chief executive Tom Harrison.
The 38-year-old Strauss retired in 2012 after captaining England to back-to-back Ashes series victories and the team's rise to No. 1 in the test rankings.
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