Since it was set up, it has been signed by 1,510,732 people.
In the description, it makes a series of unfounded allegations against Heard, who filed for divorce with Depp back in 2016.
Since their divorce, multiple stories and accusations of abuse have surfaced, with both sides making a number of allegations against the other.
Depp recently lost a libel case against the Sun newspaper and executive editor Dan Wootton.
The case centred on whether an article published in The Sun, in which Depp was called a 'wife beater', was libellous.
The newspaper claimed to have seen 'overwhelming evidence' that Depp had attacked the 34-year-old Heard, while Depp strenuously denies those allegations.
Both Depp and Heard gave evidence in the 16-day-long trial, which aired the tempestuous nature of their relationship, and stories of both brutal violence and intimate detail.
Following the trial, it was revealed that Depp had been asked to resign by Warner Bros. from his role in the upcoming Fantastic Beasts 3 movie.
The actor then went on to confirm that he planned to appeal the court case.
In a statement to his Instagram account, the 57-year-old said: "The surreal judgement of the court in the UK will not change my fight to tell the truth and I confirm that I plan to appeal.
"My resolve remains strong and I intend to prove that the allegations against me are false. My life and career will not be defined by this moment in time."
It's understood that Mads Mikkelsen will be taking over his role as the evil Gellert Grindelwald.
However, according to The Hollywood Reporter, despite his departure, the actor will still be entitled to what is said to be an eight-figure deal with the studio, meaning he'll walk away with at least $10 million (£7.6m).
Filming started for the movie on 20 September in London and Depp only shot one scene before it was announced that he will no longer play the part of Grindelwald in the J.K. Rowling series.
Depp had what is known as a 'pay-or-play contact' which requires him to be fully compensated whether or not the film is made - even if he is recast.
Following the news, thousands of people have signed another petition demanding that Depp should be brought back for the upcoming Fantastic Beasts movie.
Featured Image Credit: PA