After 21 days, the case will go to Virginia's Court of Appeals, after which the parties will have 30 days to file a notice of appeal.
Depp's lawyer Benjamin Chew previously indicated Depp would be willing to forgo Heard's payment of millions in damages if she agreed not to appeal.
"We obviously can't disclose attorney-client communications, but as Mr Depp testified … this was never about money for Mr Depp," Chew said.
"This was about restoring his reputation — and he's done that," he added.
Under the judgement order entered today, the former couple will be required to post their judgements of US$2 million (NZ$3.1m) and $10.35 million (NZ$16.3m) respectively, plus 6 per cent interest per year.
An insider told The Post that the judge had rejected all of Heard's proposed edits to the verdict on paper, and that Depp's legal team did not request an injunction against her.
The source said the court also ruled if Heard brought an appeal, she would have to post bond equal to the whole amount of the judgement plus interest payments.
On June 1, the jury found Heard had portrayed Depp "with malice" as an abuser in her 2018 Washington Post piece, injuring his career and reputation.
They also found Depp's former lawyer had defamed Heard on one occasion, and awarded her damages as part of her countersuit.
Heard's lawyer Elaine Bredehoft told NBC's Today the actress could not afford the amount she owed Depp.
She is reportedly "broke" because of the legal fees that came with the six-week trial.
Asked if Heard had the means to cover the judgement handed down by the jury, Bredehoft replied: "Oh no, absolutely not."
