Jake "Razor" Clawson (Barry Gordon) and Chance "T-Bone" Furlong (Charlie Adler) were members of Megakat City's paramilitary law enforcement agency, known as the Enforcers. They were discharged from the Enforcers after disobeying the orders of Commander Feral (Gary Owens), which resulted in the destruction of the newly built Enforcer Headquarters. While in pursuit of the criminal mastermind Dark Kat (Brock Peters), one of the main arch-villains of the series, the two rebelled against Enforcer Commander Feral's orders to fall back and leave Dark Kat to him. When they objected, citing their already-acquired target lock, Commander Feral crowded out their jet, clipping their wing and sending Jake and Chance's jet crashing into Enforcer headquarters. The resultant explosion distracted Commander Feral, allowing Dark Kat's escape. The Commander took no responsibility for the incident, discharged Jake and Chance from the Enforcers and reassigned them to work at the city's military salvage yard to pay for the damage to the Enforcer Headquarters which Feral caused.

Using discarded military parts and weapons from the salvage yard, Jake and Chance built themselves a three-engine jet fighter called the Turbokat, which resembled several different jet fighters, most notably the Grumman F-14 and the Saab Draken, along with a handful of other vehicles such as the Cyclotron (a motorcycle built into the jet's seating, deployed from the bomb bay of the Turbokat like a missile), the TurboMole (a subterranean vehicle used to drill underground), the HoverKat (a militarized hovercraft), and the Thunder Truck (a militarized Jeep modified from their tow truck). All these vehicles were stored, along with a training area and other equipment, in a secret hangar below the yard. Razor and T-Bone now patrol Megakat City as the SWAT Kats, defending it against any kind of menace that threatens the city. Their enemies include Dark Kat, the undead sorcerer Pastmaster (Keene Curtis), the mutant evil genius Doctor Viper (Frank Welker), and the robotic gangsters the Metallikats, husband and wife Molly (April Winchell) and Mac Mange (Neil Ross). The SWAT Kats also face many villains-of-the-week, such as Madkat (Roddy McDowall) and Volcanus.

The SWAT Kats keep their identities secret from everyone, including their closest ally Deputy Mayor Callie Briggs (Tress MacNeille), who assumes the responsibilities of both her post and of her boss, Mayor Manx (Jim Cummings), who mainly neglects his political duties in favor of pastimes like golf. Their methods do not endear them to Commander Feral, and the three of them often clash throughout the series. In the second season, Feral's niece Felina (Lori Alan), who holds a lieutenant rank in the Enforcers, becomes another ally of the SWAT Kats.