The project dates back to 1997, when producer Marc du Pontavice asked Jean-Yves Raimbaud to imagine 'what Tom and Jerry would look like in the year 2000,' leading Raimbaud to design a blue cat and replace the classic mouse with three mischievous cockroaches, inverting the usual predator-prey dynamic.

The series was conceived to counter the wave of superhero, manga and Franco-Belgian comic book characters popular at the time.

The three cockroaches Joey, Dee Dee and Marky are named after members of the punk rock band the Ramones.

Oggy's name is a portmanteau referencing punk/rock musicians Iggy Pop and Ozzy Osbourne, as well as Ziggy Stardust from David Bowie's 1972 album; Iggy Pop had previously sung the theme song for Xilam's earlier show Space Goofs.

After creator Jean-Yves Raimbaud's death, series director Olivier Jean-Marie chose not to alter Oggy's original design, notably keeping his blue color.

The first season cost approximately 9 million euros to produce, with production costs decreasing significantly in later seasons.

Hugues Le Bars composed the show's music for the first four seasons; after his death, Vincent Artaud took over from season 5 onward, reusing rearranged versions of the score from the 2013 Oggy and the Cockroaches movie.

Due to Hugues Le Bars' passing, new audio recordings for Oggy and the cockroach trio's vocalizations had to be made for seasons 5 to 7, though the voice actor involved remains unknown.

In March 2015, the show sparked controversy in the United States when young viewers spotted a topless woman's portrait in Oggy's caravan during an episode airing on Nicktoons; following parental complaints, Nickelodeon removed the episode from its website and broadcast rotation.

According to a 2018 Kantar-TNS survey, Oggy and the Cockroaches was recognized by 69% of French people and ranked as the most popular children's program among French households with kids, ahead of Totally Spies and Rabbids Invasion.

Several character traits echo other Xilam shows: Marky behaves like Bud from Space Goofs, and Dee Dee behaves like Gorgeous from the same series, while Oggy sometimes appears as a cameo on Bud's TV screen within Space Goofs episodes.

In 2019, to celebrate the show's 20th anniversary, the characters were immortalized as wax figures at the Musée Grévin in Paris.