The Tranmere Rovers manager has until April 8 to respond to the charges.
The League One club suspended Moore last month when the FA revealed it was launching a probe over allegations he broke rules by betting in a competition in which Tranmere were involved.
Moore, who had two spells in charge of Rotherham as well as managerial stints at Southport and Oldham, was in charge at Prenton Park between 2006-09 before returning for a second spell at the helm in 2012.
Assistant manager John McMahon has been in temporary charge at Prenton Park during Moore's suspension, with Tranmere currently 20th in the table, one place above the relegation zone on goals scored.
Current regulations prohibit players, managers and club officials from betting on competitions in which their teams are involved.