In the new documentary “Elephant,” now streaming on Disney+, we follow a herd of the enormous, big-hearted African animals who annually journey thousands of treacherous miles across the Kalahari Desert for a drink of water and a bite to eat.

“They travel such huge distances,” co-director Mark Linfield tells The Post. “Botswana to Angola, down to Zimbabwe and back to Botswana.”

In order to capture that epic, little-known migration, Linfield had to go the distance, too, moving to Africa from Britain with his wife and co-director, Vanessa Berlowitz, and their young son. The crew, including about 20 other intrepid filmmakers, tagged along with the pack of pachyderms for close to three years.

“We actually moved lock, stock and barrel with our family, with our then 7-year-old, so we could live in Africa and go on the journey with the elephants,” Berlowitz says. “We spent enormous time in the bush, home-schooling our kid as we went.”

The pair of experienced nature documentarians chose which herd to follow with the help of Mike Chase, a scientist from the nonprofit Elephants Without Borders. Chase, who has spent years observing elephants in the field and using satellite telemetry to track their journeys, found the ideal group for a family-friendly Disney story.

The doc, narrated by Meghan Markle (billed here as Meghan, Duchess of Sussex), centers on Shani, a mother elephant, and her cub Jomo, as they’re led by 50-year-old matriarch Gaia from Botswana’s Okavango Delta to find sustenance. On this unique trip, the filmmakers were gobsmacked by their amazing discoveries.

In one moving scene, the herd encounters a graveyard with bones of elephants they likely previously encountered as living animals. Each one touches the bones with their trunk, as though paying respects at a funeral.

“Not many animals can surprise you,” says Linfield. “But elephants, out of nowhere, will do something like that that completely blows you away.”

Later on their trek, the adorable Dumbos have a run-in with long-lost relatives, and we watch them “hug” and even crack smiles as they chat with their cousins. “That concept of ‘an elephant never forgets,’ ” says producer Roy Conli. “They do remember!”

Following Gaia, Shani and the rest through the unpredictable African wilderness proved challenging at times for the filmmakers. Occasionally, it would take several days to move their equipment only a few hundred feet to get the perfect shot.

“The elephants are one side of a hippo and crocodile-infested river, and you can’t cross it even with a canoe because the hippos would overturn it,” Linfield recalls. “You got to use planes and boats and helicopters.”

But it was never a leap getting up close and personal with the big guys.

“The fundamental rule of filming elephants is let them come close to you,” Berlowitz says. “I’m amazed they allow these irritating humans to be around them!”