Lindgren and Lagerkvist of the Stockholm-based studio say the collection came about after Moooi co-founder Marcel Wanders approached them to create a lighting and furniture collection that would appeal to anyone.
"Marcel said: 'Make us a lamp that even my grandmother would like,'" Lagerkvist explains in the movie.
"Our first thought was to make something that is taken from nature and just presented as a piece of furniture. When we presented it to Marcel, he just loved it."
However, Lindgren admits that the unusual designs were "a bit of an experiment" and says that, while she was certain people would react strongly to the collection, she was not at all sure whether those reactions would be positive or negative.
"Our idea was that people will either love it or hate it," she says.
In fact, the collection proved a big hit, with the Horse Lamp in particular being regularly featured in magazines around the world.
Lindgren believes the playful nature of the lamp is what appeals to people.
"People are sending us photos from all over the world riding on our lamp," she says. "It's amazing, we never thought it would have that sort of life."
Front worked with a sculptor to create the lifesize animal models, which are manufactured from black polyester, supported by a metal frame inside.
Numerous imitations have sprung up after the collection's success, but a genuine Moooi product can be distinguished by a number of raised circles on the surface.
"We added dots to the animals to make them more of a product of Moooi," Lagerkvist says. "That's been very valuable because these pieces have been heavily copied."
This video interview was filmed by Dezeen in Milan.
Most Loved is a collaboration between Dezeen and car brand MINI celebrating design objects that have found a special place in people's hearts. We will be interviewing some of the world's leading designers about their most popular and enduring designs.
You can watch all the movies as we publish them on our special Most Loved microsite: www.dezeen.com/mostloved