Campbell, 45, took over as Southend manager in October last year but won only four of his 23 games in charge.
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Southend were relegated from League One (third-tier) after the season was called off due to the COVID-19 pandemic.
"Sol's use of the club's young talent was a breath of fresh air who responded well to his stewardship," a spokesperson for Southend said in a statement.
The club wishes to thank Sol and wish him, together with his management team, well for the future.
Campbell picked up his first win against Wimbledon in the EFL Trophy in November last year, while his first league victory came against Accrington Stanley in January.
"I have really enjoyed my time at Southend and whilst it was a difficult time fighting relegation, I still enjoyed the experience," the former Arsenal and England defender said.
"... The club have an exciting future with the plans for the new stadium in place, but with the COVID-19 situation having a profound effect on businesses, I am keen not to be a financial burden."
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