All the prints were marked as "out of stock" by Thursday evening. There were 780 pieces of art. Buyers paid £14,950 for a set of all four framed prints or £3,950 for a single print, news agency AFP has reported.
The gallery chain later posted a tweet saying that "Johnny Depp broke the internet" and its website had crashed due to demand.
The works depict Bob Dylan, the late actress Elizabeth Taylor, actor Al Pacino and Rolling Stone Keith Richards.
Depp's collection of prints called "Friends & Heroes" was "a testament to those he has known well and others who have inspired him as a person".
For Johnny Depp there has always been art. Before acting, and before music, art has always been an important outlet for his creativity. While his acting repertoire is the foundation for his fame, the recent reception to his music with Jeff Beck has encouraged him, and emboldened him, to share his art, the Castle Fine Art website writes.
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It further wrote, “Each image is an intimate reflection of their character in Johnny's eyes; a portrayal of how they have revealed themselves to him. From his dear friend Keith Richards, who inspired the mannerisms of the infamous Captain Jack Sparrow, to Bob Dylan, whose creative influence on the artist is seen in his vivid and immortal portrayal by Johnny."
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The gallery quoted Depp as saying: "My paintings surround my life, but I kept them to myself and limited myself. No one should ever limit themselves."
The 59-year-old "Pirates of the Caribbean" star has spent millions on a bitter legal battle with his ex-wife, the 36-year-old actress Amber Heard.
Depp in June won an award of $10 million in a defamation case against Heard in the United States, while she won $2 million in damages after counter-suing.
Heard is appealing against the verdict of the jury trial, which was live-streamed to millions and featured lurid and intimate details about the former couple's private lives.
Depp previously lost a libel case against the British tabloid The Sun in London in 2020 for calling him a "wife-beater".
In another creative venture, the actor this month released an album with English rocker Jeff Beck.
The record has been poorly reviewed by critics but broke into the top 40 in the UK.
(With inputs from AFP)
