The Pirates of the Caribbean actor’s post marks his first foray into the world of social media, and his account quickly racked up more than 2.2m followers.
“Before I go, on a more suppose personal note: thank you all for your kindness, your unwavering support and your strength over these years,” he said.
“I am touched beyond words.”
Depp is embroiled in a legal case with Heard, whom he’s suing for $50m (£40m) after denying claims that he physically abused her.
Depp and Heard met on the set of 2011 comedy The Rum Diary, and married in Los Angeles in February 2015.
In May 2016, Heard obtained a restraining order against Depp after her initial accusation of abuse.
The couple settled their divorce out of court in 2017, with Heard donating her $7m (£5.5m) settlement to charity.
Depp also recently sued the publishers of The Sun and its executive editor, Dan Wootton, over an article which alleged he had been abusive to his former wife.
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