In December, Ms Heard, also an actor, wrote an article for The Washington Post describing the backlash she faced due to speaking out about domestic violence.
Mr Depp's lawsuit says he "never abused Ms Heard" and the claims are "part of an elaborate hoax" to advance his ex-wife's career.
He is seeking $US50 million in damages.
Ms Heard first accused Mr Depp of domestic violence in May 2016, the year after they were married. Mr Depp was ordered to stay away from her and the couple divorced in 2017.
