Depp lost a libel case less than two years ago against the Sun, a British tabloid that labeled him a "wife-beater." A London High Court judge ruled that he had repeatedly assaulted Heard.
Depp's lawyers filed the U.S. case in Fairfax County, Virginia, because the Washington Post is printed there. The newspaper is not a defendant.
Both sides have claimed damage to their Hollywood careers.
Heard's legal team presented an entertainment industry expert who estimated that the actress has suffered $45-50 million in lost film and TV roles and endorsements.
An industry expert hired by Depp's side said the actor has lost millions because of the abuse accusations, including a $22.5 million payday for a sixth installment of "Pirates".