A solitary second-half goal from Argentine striker Mauro Boselli sent the match into extra-time before Juan Ignacio Gonzalez's 112th-minute header secured a 4-3 aggregate win for the visitors.
Leon, who finished eighth during the regular season, became the first club since Pumas UNAM in 2004 to secure the league double, having clinched the Apertura title in December.
Gustavo Matosas' men went into the match needing to overturn a one-goal deficit after losing 3-2 at home to Pachuca in the opening leg on Thursday.
And while the game was played at a frenetic pace, neither side could break the deadlock during the opening 45 minutes.
Leon eventually got their goal in the 66th minute through Boselli, who sent the match to extra-time due to the fact that away goals do not apply in the Liga MX decider.
Pachuca had their chances throughout the contest, forcing Leon goalkeeper William Yarborough into a number of saves.
But they were punished for their lack of conviction in front of goal, with Gonzalez scoring 10 minutes from time to hand Leon a memorable victory after accounting for top seeds Cruz Azul and Toluca en route to the final.
