The news comes just four days after chairman Ron Martin staved off an application to put the club into administration from HM Revenue & Customs.
They must still deal with a winding-up petition put forward by Charterhouse Commercial Finance Plc, with the hearing scheduled for 11 August.
Martin says all debts have been successfully paid by the club thanks to a partnership with supermarket giant Sainsbury's.
In addition to Bilel and Bouzid, the players Southend have signed are: Chris Barker, Josh Simpson, Mark Phillips, Luke Prosser, Louie Soares, Graham Coughlan, Rhys Evans, Glenn Morris, Sean Clohessy, Craig Easton, Sofiene Zaaboub, Ryan Hall, Blair Sturrock, Peter Gilbert and Barry Corr.
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