Campbell had been interviewed by the League One club and was made a candidate to replace the departed Kevin Bond, who resigned in September.
Campbell has been without a club since leaving Sky Bet League Two side Macclesfield Town by mutual consent in August.
Southend chairman Ron Martin recently spoke glowingly of Campbell, praising the work he conducted at Macclesfield.
"Sol is a passionate, eloquent individual," Martin had told the Southend Echo.
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