Heard's legal team submitted the appeal notice on Thursday to the Virginia Court of Appeals, seeking to overturn the lower court's June 1 ruling.
After a six-week televised trial, a seven-person jury concluded that Heard defamed Depp, and the Pirates of the Caribbean star was awarded $US10.35 million ($A15 million) in damages. The jury also determined that Heard was defamed, awarding her $2 million.
Heard's lawyers had argued she had told the truth and that her comments were covered as free speech under the US Constitution's First Amendment.
Her team said it sought to ensure fairness and justice through the appeal.
"We believe the court made errors that prevented a just and fair verdict consistent with the First Amendment," a spokesman told Reuters. "We are therefore appealing the verdict."
Depp's team said it was undeterred by the appeal.
"We remain confident in our case and that this verdict will stand," a spokesperson for Depp said.
The filing comes more than a week after a judge rejected Heard's request for a new trial. Her lawyers had argued that one of the jurors had served improperly.
During the trial, Depp said he never hit or sexually abused Heard and argued she was the one who became violent during their relationship. Heard said she had slapped Depp but only in defence of herself or her sister.
Depp faced a different outcome in Britain less than two years ago, when he sued the Sun tabloid for calling him a "wife beater". A London High Court judge ruled he had repeatedly assaulted Heard.
After the US ruling in June, Heard lawyer Elaine Charlson Bredehoft accused Depp's team of suppressing evidence that was allowed in the British libel case.
