The risk management businessman replaced David Peever in October as interim chairman after the former mining executive was forced to quit in the wake of a scathing governance review of the board's culture and operations.
Eddings's role was made permanent a month later but his appointment was rejected publicly by Cricket Victoria in a blow to his authority.
Eddings' chairmanship was confirmed in a CA media release on Tuesday which said he had resigned as Victoria's director on CA's board.
"CV (Cricket Victoria) supports CA's decision to appoint Earl as an independent director and looks forward to working with him and the CA Board as we continue to grow Australian Cricket," Cricket Victoria Chair and CA Nominations Committee member Paul Barker said in the release.
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CA has seen a slew of top executives and board members depart since the ball-tampering scandal erupted in Cape Town in March 2018, which prompted the Longstaff review into the board's culture.
Long-serving CEO James Sutherland stepped down to be replaced by his former deputy Kevin Roberts, former high performance boss Pat Howard was sacked, while former Australia captain Mark Taylor quit as a board director in November.
CA said Richard Freudenstein, a former senior executive at media giant News Corp, had replaced Taylor as New South Wales state's director on its board.
CV will look to appoint a new director in the wake of Eddings's resignation.
(Reporting by Ian Ransom; Editing by Peter Rutherford)
