"When the successful male mated with the female he came in from above and behind her ... he clasped her between his pectoral fins and whilst they floated along together he was stroking her flanks with his pectoral fins," he says.
A gallery of the images will make their first public appearance at Auckland Museum tomorrow. National Geographic Channel will also be screening footage shot by marine wildlife consultant David Donnelly, alongside Edwards' images on Sunday at 7.30pm.
National Geographic says scientific data gathered during the research trip has been provided to humpback whale researchers around the world. More is known about the gestation period of the species - which is roughly 11 months - than is known about their copulation.
Despite humpback whales being renowned for their song, Edwards says no sound was heard during the act, although it may have been at a frequency inaudible for humans.
The only sounds heard came from the female blowing bubbles from her mouth after copulation.
"The purpose of this bubble release is still unclear however it may have signalled to the male that the reproductive act was over. Further research is still needed to confirm whether this is a common sexual practice or simply a random occurrence," Edwards says.
"When we came upon the heat run, it was the last day of my shoot. I didn't have a single frame of these animals from the whole trip. All I kept thinking was 'don't mess it up'. I was just supremely lucky to even be there, let alone capture this incredibly intimate moment on camera.
"I've been doing this for decades now and it's amazing how often the thing you are looking for happens on the last day or in the last hour."
The Australian's career as a wildlife photographer began when he was a keeper at Melbourne, taking photos of the captive animals in the late 1980s.
"Photography is an obsession for me. Once I had that job all the money I earned was spent on camera equipment and travel. So I was working in the field pretty quickly."
Edwards has been shooting for National Geographic for about 15 years, the dream job for an enthusiastic natural history photographer. He has also worked for the Australian Geographic, Sports Illustrated, BBC Wildlife Magazine, The New Yorker, and Conde Nast Traveller.
"I've shot species unknown to science before and species on the brink of extinction, and the nice thing about photographing those sort of animals is you feel that you can make a difference with the pictures. You can show people things that they might not have the opportunity to see and also people might get in behind supporting research projects on them," he says.
"The animals that are the most difficult to get great shots of you seem to get more joy out of the pictures. If you suddenly get a tiny grassland bird that sits on a perfect reed, all of a sudden the picture becomes special because of the difficulty of [taking] it."
Taking beautiful images of animals in the wild poses plenty of risks, and Edwards says his "list of stupidity is long and varied". He has had close calls with bad-tempered snakes, territorial hippopotamuses, and has been chased by lions, but Edwards says it is the little things that pose the most danger.
"It's the aquatic spider bites that don't heal for three or four months. It's the blood-borne viruses ... I had one virus that by the time it was done it had wiped a year of memory that I never got back. I've had insects crawl in behind my eyes and live in behind there. I've had more diseases than you can poke a stick at. It is the unseen things that risk your life greater most large animals.
"I had a tick infestation that we couldn't get rid of for nine months. I even bought my wife a pair of tick tweezers."
The job also means a lot of time away from family and friends in Melbourne.
"I could be away for months with no contact back home," he says. "I sat in a tree once for five and a half weeks. There was no one to talk to out there.
"My career has been a way of life, not the work that I do."
When giving advice for budding wildlife photographers, Edwards says "less is more".
"Digital photography has just opened up so many possibilities for people, but at the same point in time people aren't really learning the art of photography because the cameras are so clever.
"It is so important to get it right at the time in the field. Do not photograph something knowing that you can fix it or manipulate it when you get back, because that is not teaching you anything about the subject matter that you're shooting, and more importantly, about the art of photography."
Edwards says minor treatment to images on the computer is fine, but too much processing means the image does not accurately reflect the reality of the natural world.
"Just treat them gently and you get a much more beautiful, realistic picture. There is a lot of material around at the moment that is so heavily manipulated that it just destroys the actual integrity of the image."
