First major user of magick in the DC Universe was Doctor Occult (More Fun Comics #6, 1935).
The character first appeared in New Fun Comics #6 in 1935. He was a supernatural detective, whose detecting style was very much in the style of Sam Spade, only with supernatural abilities. He was assisted by his butler Jenkins in one adventure. His girlfriend/partner called Rose Psychic appeared in his first adventure and then returned again later in the series.
He also appeared in Centaur Publications' The Comics Magazine #1 under the name "Dr. Mystic". This was the same character because his story, "The Koth and the Seven", began in The Comics Magazine and continued in DC's More Fun Comics #14-17 (issues also designated as vol. 2, #2-5). In this story, he travels to a mystic realm where he flies and wears a cape, making him the first caped comic book superhero. This story also introduced the Seven, a group of mystics who would later be retconned into having raised Richard Occult and Rose Psychic. Doctor Occult made his last original appearance in More Fun Comics #32 in 1938.
He later appeared in Crisis on Infinite Earths (1986), The Books of Magic (1991), Vertigo Visions: Dr. Occult (June 1994), and The Trenchcoat Brigade (1999).
Marvel's first well known magic user is the famous Dr. Stephen Strange who debuted in Strange Tales #110 (July 1963). The good Doctor would herald in an entire age of new magical menaces, visionary worlds and long-lived memes of the Marvel Universe. These would include: The Dark Dimension and its terrifying master, the Dread Dormammu, Nightmare and the Nightmare Realm, The Undying Ones, Baron Mordo, The Enchantress and the Doctor's one great love, Clea.
The character, created by writer-artist Steve Ditko with dialogue by editor-writer Stan Lee, debuted in Strange Tales #110 (July 1963), a "split book" shared with fellow Marvel character the Human Torch until issue #134 (July 1965), and then super-spy Nick Fury until issue #168 (May 1968). Strange appeared in issues #110-111 and #114 before the character's eight-page origin story appeared in #115 (Dec. 1963).