it's not quite that simple.
The first ones, when he came back to the stage in 1969, were plain two-piece outfits (herringbone trim on the collar and chest vee) in black, white, and navy, and they were very much modeled on a karate gi, complete with a belt reminiscent of karate belts. They had godets (kickpleats) with satin inserts on the pants and French (I think) cuffs with buttons (some later jumpsuits skipped the buttons), but the collar was nowhere near as high as in later iterations. The basic design was probably Elvis' idea, strongly influenced by his background in martial arts. He also wore, for some of the shows, two-piece outfits based on the cut of the black leather suit he wore in his 1968 TV special that, in turn, was based on a Levi's denim jacket and jeans, though the 1969 stagewear had somewhat flared pants and he wore wide leather belts with studs and chains, and lionheads, with those suits (he was wearing these belts offstage at the time but they were the same kind of belts he'd come back to wear onstage starting in late 1971, the classic Elvis stage belt). He accessorized with designer silk scarves (Hermes, Bill Blass, etc) and, in later years when he began regularly throwing them to the audience, went from purpose-designed 36x36" silk scarves to less expensive satin.
Here's one of the 1969 karate-style suits:
When he returned to Vegas in January, 1970, he was wearing one-piece jumpsuits, all but one with the classic Napoleonic collar. I'm not sure who made the decision to go one-piece...Priscilla's claimed she designed the first suits, but she claims a lot of things and the more likely truth is that Elvis talked to his designer, telling him what he needed (based on the first season of live performing) and they came up with a solution. The jumpsuits eventually evolved into studded suits (with capes coming in late in 1971), then suits laden with studs and jewels (Austrian crystals and semiprecious stones) that were very heavy (and featured heavy capes) and, finally, intricately embroidered suits that were lighter but very expensive. The flares got bigger in 1971, bigger still in 1972 and beyond but, otherwise, the basic design of the suits (tight around the midsection and hips, loose in the chest and shoulders to accommodate movement) remained the same. These suits were an evolution of the 1969 design but Elvis liked the jumpsuits better because they tended to maintain their structural integrity during his onstage workouts...the material had some stretch to it and so offered support and freedom of movement. He had a problem with ripping pants, throughout his career, because of his moves, and the jumpsuits minimized that. When he went back to wearing pants and shirts onstage in 1972, for a while, he split so many pairs of pants that he went back to jumpsuits for the rest of his career.
I think the fact that his costumes were made by IC Costumes of Hollywood ('IC' standing for IceCapades) had something to do with it, too. After all, one-piece suits were not uncommon in skating and the material used for Elvis' suits -- wool gabardine -- was also what was used for skater's suits. That's something a lot of people assume wrong about, actually...Elvis never wore polyester jumpsuits (probably rarely, if ever, wore polyester at all, even in the '70s -- IC Costumes not only made his stagewear but made most of his offstage attire, too, designed by the same people who designed the jumpsuits); all of the material used on his suits was imported from Milan, a custom blended wool gabardine that included a bit of spandex for stretch. Add in the crystals and jewels he used later, some of them extra-expensive dichrotic stones, and it's easy to see where the materials cost of his suits came from. Some of the suits were allegedly as much as 40 lbs in weight, with cape. Elvis stopped wearing the capes in 1973 because they got too heavy and because they were a hazard (fans would grab them and almost pull him off the stage).
Example:
Had he lived, I think he'd have ditched the jumpsuits at some point, as iconic as they became in their own right. In the meantime, he influenced the dress of a lot of other pop, soul, and rock acts of the '70s (the Osmonds even went to the same designer -- Bill Belew, whose association with Elvis began with the 1968 TV secial -- for their outfits).
Hey...you asked. :D