In the scripted video, the actors describe Australia as a "wonderful island" and warn others to respect its laws.
The video was submitted to the court as Ms Heard escaped conviction for failing to declare the couple's dogs Pistol and Boo when visiting Mr Depp in Queensland in a private jet in May.
Reaction on social media was swift and brutal, with many comparing the short film to Chinese or North Korean-style propaganda. Viewers were divided over Mr Depp's somewhat lacklustre performance.
"I've seen IS (so-called Islamic State) hostage videos with more joie de vivre than Johnny Depp's apology," said one Twitter user.
Others suggested sarcastically that the low-budget feature was his finest and most innovative role in years.
Some tried to imagine the scene behind the camera.
The video was shot on Australia's Gold Coast on Sunday and played during the hearing at Southport Magistrate's Court.
It begins with Ms Heard describing Australia as a "wonderful place with a treasure trove of unique plants, animals and people".
Johnny Depp continues: "Australians are just as unique, both warm and direct. When you disrespect Australian law, they will tell you firmly."
This was widely seen as a reference to Barnaby Joyce, who as agriculture minister had originally threatened to have Pistol and Boo put down if they didn't "bugger off" back to the United States.
Mr Joyce, who is now deputy prime minister, acknowledged that the video may not have been entirely natural. "I don't think it would be something they would have willingly wanted to do," he said.
People have poked fun at the case since it began last year, using the hashtags #WarOnTerrier and #Terriergate.
It is not clear whose idea the video was, but reports said Australian prosecutors had vetted the dialogue.
Ms Heard pleaded guilty to falsifying an immigration document. The more serious charges of illegally importing animals were dropped.
The judge in the case placed Ms Heard on a A$1,000 ($770; Â£540) good behaviour bond on Monday. No conviction was recorded against her.

The 35-year-old, who missed the second half of last season with a knee injury, has committed to Swiss Indoors until 2019.
Federer, who returned to action in January, won his first Grand Slam title since 2012 and his 18th in total with victory in the Australian Open.
"Playing in Basel is always a highlight of the year," he said.
He has won Swiss Indoors seven times since making his debut in the tournament in 1998.
He is scheduled to return to action next week at the Dubai Duty Free Championships.
"If I am spared again by the injuries, I am convinced that I am still capable of beating the best players in the world in the big tournaments," he said in January.
Tennis correspondent Russell Fuller
Federer's first appearance in his home tournament was in 1998, where as a 17-year-old he was beaten in straight sets by Andre Agassi.
There is, of course, no guarantee Federer will be on the Order of Play in 2019, but this is another reminder of his long-term thinking.
He missed the last six months of 2016, not just to allow his knee to recover, but also with preservation of his body in mind. At one stage, the conversation revolved around whether Federer would make it to the Rio Olympics. It is time to start the debate about Tokyo.
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Johnny Depp and Amber Heard have released a stilted apology video for breaking Australia's strict biosecurity laws, bringing a bizarre end to the so-called "war on terrier".
[NEXT_CONCEPT]
Roger Federer has signed a three-year deal to play at his hometown event in Basel until the age of 38.