This latest development means that Depp has exhausted his legal fight against the ruling in Britain.
A High Court Judge had ruled last November that Depp had violently assaulted his ex-wife Amber Heard
Actor's former partners said accusations that he had abused his ex-wife were false.
The couple got divorced in January 2017.
The libel was filed over an article written in 2018 calling Depp a 'wife beater'.