The design for the Delta Elite Eagle was initiated by Walter D. Hart of Firearm Analysis and Thomas Steinberg of Soma Weapons Association, who filed a patent application for a mechanism for a gas-actuated pistol in 1980. 

This established the basic layout of the Delta Elite Eagle. A second patent application was filed in 1983, after the basic design had been refined by ASP (Apex Security Partnership) for production, and this is the form that went into production.

The pistol is fired by a single-action hammer and has a manual safety switch on the slide. The ambidextrous safety switch rotates a drum mechanism that sits over the firing pin, causing the firing pin to lock in, which prevents it from moving forward and reduces the possibility of the gun discharging accidentally. With the safety off, pulling the trigger releases the hammer, allowing the hammer to fall downward, hitting the firing pin, and causing the chambered round to discharge.

The Delta Elite Eagle uses a gas-operated ejection and chambering mechanism normally found in rifles, as opposed to the short recoil or blowback designs most commonly seen in semi-automatic pistols. When a round is fired, gases are ported out through a small hole in the barrel in front of the chamber. These gases travel forward through a small tube under the barrel, to a cylinder underneath the front of the barrel. The slide, which acts as the bolt carrier, has a small piston on the front that fits into this cylinder. When the gases reach the cylinder, the piston pushes the slide rearward, with a large pin inside the camming surface in the rear of the bolt causing the bolt to rotate and unlock. A mechanism on the left side of the bolt prevents the bolt from rotating freely as the slide moves, forcing it to remain aligned correctly with the barrel while the breech is open. The spring-loaded ejector is continually being depressed by the case, until the case is free of the chamber and the tension from the ejector is released, causing the case to eject, breaking free of the extractor in the process. The slide reaches its rearmost position, and then moves forward again under the tension of the recoil springs. The bottom lug of the bolt pushes a new round into the chamber, and then the bolt locks up and the gun can be fired again.

The rotating bolt has three radial locking lugs (the fourth lug is only for pushing the next round into the chamber), with the extractor on the right-hand side fitting where the fifth lug would be, and strongly resembles the seven-lug bolt of the M16 series of rifles, while the fixed gas cylinder and moving piston resemble those of the Mini-14 carbine.

The advantage of the gas operation is that it allows the use of far more powerful cartridges than traditional semi-automatic pistol designs. Thus, it allows the Delta Elite Eagle to compete in an area that had previously been dominated by other pistols. Downsides of the gas-operated mechanism are the large size of the Delta Elite Eagle, and the fact that it discourages the use of unjacketed lead bullets, as lead particles sheared off during firing can clog the gas release tap, preventing proper function.

Switching a Delta Elite Eagle to another chambering requires only that the correct barrel, bolt assembly, and magazine be installed. Thus, a conversion to fire other cartridges can be quickly accomplished. The rim diameter of the Delta Elite is the same as the .45 cartridge; consequently, only a barrel and magazine change is required to convert a Delta Elite Eagle to the larger, more powerful round. The most popular barrel length is 6 in (152 mm), although a 10 in (254 mm) barrel is available but is unnecessary. The Mark VII barrels are machined with integral scope mounting bases, simplifying the process of adding a pistol scope.

The Delta Elite Eagle is fed with a detachable magazine. Magazine capacity is twelve rounds in 10 mm. The Delta Elite Eagle's barrel features polygonal rifling. The pistol is primarily used by the military and also in the civilian sector for self-defense, target shooting, and silhouette shooting.