Jonathan Tweet invented 3e’s core mechanic and its DC concept
Difficulty Class did indeed make its D&D debut in 3e,1 and has been traced by Shannon Appelcline's historical work directly to Jonathan Tweet, lead designer of Dungeons & Dragons 3rd Edition.
Initial 3e work began without a design vision shortly after WotC acquired TSR, and CEO Peter Adkison stepped in to give an overall goal and philosophy and to install Tweet as the lead designer. Tweet proceeded to establish the core mechanic — and hence Difficulty Class — as “die + bonus”, a core mechanic initially developed by Tweet for and appearing in the first edition of Ars Magica.
Appelcline in his own words, from Designers & Dragons: The '90s, pages 155–6:
Peter Adkison — who had previously left third edition design work to Bill Slavicsek and a group of ex-TSR employees — decided to write a basic philosophy for the new edition that would guide future work. […] He called for a new game that would keep the feel of the original D&D rules, but would throw out things that didn't make sense. He also named Wizards of the Coast RPG head Jonathan Tweet as the new leader of the third edition project. […]
Using lessons learned from Alternity, it offered a unified task-resolution system. The core mechanics were drawn from the “die + bonus” skill system that Tweet had created for Ars Magica (1987) over a decade before. Its main difference from Alternity was that it was a roll-over system rather than roll-under: skills were added to die rolls and compared against either target numbers or opposed skills.
Though the inspiration for using a unified mechanic came from Alternity, that system doesn't feature DCs or an equivalent, instead having you roll under your own ability or skill scores to achieve a success. Flipping it around to use his “die + bonus” roll-over mechanic required a target number external to the character, as in Ars Magica — and by Tweet importing that design, thus did Difficulty Class enter into D&D's design DNA in 1999 and lives on to this day.
As an editorial note, I find it interesting that today it is Difficulty Class that we consider characteristic of this task resolution system. At the time, Tweet's own conception of the mechanic's innovation wasn't DC, but the idea that situational effects were reflected in a unified modifier (rather than alternative die sizes or modifiers on your stats, mixed with a few low-value straight roll bonuses). DC was just a necessary invention to accommodate that design. So although DC is the most visible characteristic of this core mechanic, this is somewhat backwards historically, as the original heart of the mechanic lies elsewhere.
Appelcline talks about this innovation within the RPG design context of the late 1980s — and credits it as an innovation of Tweet's — more in the 80s volume of Designers & Dragons on page 307, in the history of the publisher Lion Rampant2:
One of the notable innovations of Ars Magica was Jonathan Tweet's target-based skill roll (or, “die + bonus” as Tweet calls it). Early RPG systems had mostly used simple roll-under mechanics (e.g., percentages) or roll-over mechanics (e.g., THAC0). They were ultimately limited in range by a die roll, and initially offered no opportunities for comparison contests. These early systems were now being innovated by games like Pendragon that used a roll-under-and-highest-roll-wins mechanic for competitions.
Tweet felt the need to have contests, modifiable rolls, and results that weren't bound by die size. He introduced “die + bonus” and targets in Ars Magica. The idea was a wave that hit the industry at the time; it can also be found in Bard Games' Talislanta (1987) and R. Talsorian's Teenagers from Outer Space (1987) and Cyberpunk (1988).
As obvious as design as it seems like today to have an uncapped bonus added to a die roll, it was something new under the sun in RPG design at the time. We can thank Jonathan Tweet for the idea of rolling and adding a small-or-large modifier in RPG mechanics, and the Difficulty Class that fell out of that design goal.
1. Though D&D has had “target numbers” in its DNA since the beginning, that's unavoidable in most dice systems — you need a number that separates failure and success. The particular core mechanic that made DC prominent and explicit was indeed new in 3e.
2. Lion Rampant was founded by Jonathan Tweet and Mark Rein•Hagen (of Vampire: the Masquerade fame) to design and publish Ars Magica, “a game that did wizards right” (qv. Appelcline). While Rein•Hagen was the creative visionary, Tweet was the meticulous mechanics designer.