The Alpha Leonis system (or Regulus system) was an inhabited planetary system. This system was located in the Alpha Quadrant. There were two known planets that supported life: Regulus III and Regulus V. Notable forms of life in this system included the eel-birds of Regulus V and the Regulan bloodworms. This system was located three hundred light years from the Bajoran system and was located within 90 light years of the Sol system. Its location in the Milky Way Galaxy was depicted on a Federation star chart in 2293. (TOS: "The Cage", "Amok Time", "The Trouble with Tribbles"; Star Trek VI: The Undiscovered Country, production art; TNG: "The Vengeance Factor"; DS9: "Fascination"; ENT: "Two Days and Two Nights", "Kir'Shara")
In 2154, a Vulcan High Command attack fleet massed in this system in preparation for an abortive preemptive strike against the Andorians. The Regulus system was the closest accessible system that was known to be outside the maximum range of Andorian Imperial Guard listening posts. (ENT: "Kir'Shara")
The association between Alpha Leonis and Regulus is based on reference material and the real world association. It has not been confirmed in canon. According to Star Trek Maps (pg. 29), The Worlds of the Federation (pg. 130) and Startrek.com, Alpha Leonis was the same system as Regulus. Alpha Leonis was the Bayer classification name for Regulus. 
According to the Star Trek: Star Charts (pgs. 56,61,62), the Regulus (or Alpha Leonis) system was located in the Beta Quadrant. This was a trinary star system. Regulus A was a B-class star with a magnitude of +1, which was a hundred times brighter than Sol. Regulus B was a M-class star. Regulus C was a K-class star. In 2152, this system was in non-aligned space. Between 2152 and 2378, this system was incorporated into Federation space, and was a destination on the major space lanes.
"The Explored Galaxy" was a map of charted space in the Alpha Quadrant. Regulus was located between the Tholian Assembly and Romulus. Both locations were identified in DS9: "The Search, Part II", "Call to Arms" as being located in this quadrant. This chart was also seen in several Star Trek: The Next Generation and Star Trek: Deep Space Nine episodes set in the 24th century, from the year 2364 to 2370. These were: TNG: "Conspiracy", "The Measure Of A Man", "The Emissary", "The Mind's Eye", "The Game" and DS9: "In the Hands of the Prophets", "Cardassians".