Heard, 29, and the "Black Mass" star both attended Southport Magistrate's Court in Queensland state on Monday, said The Hollywood Reporter.
The presiding judge dropped two illegal importation charges against the actress.
The presence of Pistol and Boo in Australia caused a furor last year when then Federal Agriculture Minister Barnaby Joyce threatened to deport them or have them put down.
"The Danish Girl" actress brought the dogs into Australia on Depp's private jet on a visit while he was filming "Pirates of the Caribbean: Dead Men Tell No Tales," without permits or a period in quarantine, flouting Australia's strict animal import laws.
"Ms Heard has made a video, the significance of which will become apparent... It relates to an expression of remorse and recognition of the importance of compliance with Australia's border protection laws," said Kirk.