In a joint statement, the pair acknowledged their relationship had been volatile.
"Our relationship was intensely passionate and at times volatile, but always bound by love," it read.
Lawyers for Heard filed a motion on Tuesday to dismiss a temporary restraining order against Depp.
News of the divorce settlement came just a day before a hearing regarding the restraining order was due to begin.
The temporary order had ordered Depp not to contact Heard, and stay 100 yards away from her, after she accused him of striking her and throwing a mobile phone during a fight earlier this year.
The Hollywood star, 53, had always denied abuse allegations made by his former wife.
Heard, 30, filed for divorce in May and obtained the temporary restraining order against Depp a few days later.
The couple, who were married for just under 18 months, also came to a financial settlement as part of their divorce.
Unconfirmed reports put the value of the settlement between $7 million (Â£5.4 million) and $7.7 million (Â£5.9 million).
"Neither party has made false accusations for financial gain. There was never any intent of physical or emotional harm," the statement continued.
It said Heard would be donating proceeds from the divorce settlement to an undisclosed charity.
Neither of the actors said they would comment further on the case.
Depp has two children from a previous relationship with French singer and model Vanessa Paradis.
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Johnny Depp and Amber Heard have settled their divorce, saying neither of them intended to cause the other any physical or emotional harm.