Mandaric, along with Tottenham Hotspur manager Harry Redknapp, already faced two counts of cheating the public revenue, while Storrie had already been charged with tax evasion over a 2003 transfer deal.
A hearing at Southwark Crown Court, which the men did not attend,was told Mandaric and Storrie have now also been charged with evading tax in relation to midfielder Eyal Berkovic's termination fee and will appear at City of Westminster Magistrates' Court on June 17 and June 9 respectively.
The pair are accused of making an offshore payment to terminate Berkovic's contract on which no tax was declared or paid, the Press Association reported.
Serbian-American businessman Mandaric, who is now chairman of Leicester City, took over Portsmouth in 1998, injecting life into the English south-coast club, which won promotion to the Premier League in 2003.
The team has been in turmoil this season. With debts of more than £199 million Portsmouth became the first Premier League club to go into administration and were relegated after finishing bottom of the league.
Storrie stepped down as chief executive of the troubled club in March.
All three men will appear at Southwark Crown Court on September 14.
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