The University of Nuevo Leon side won the final 4-1 on aggregate following their 1-0 first leg victory away to Santos in Torreon on Thursday.
Tigres, whose previous titles came in 1978 and 1982, lifted their first crown since the introduction of two championships per season in 1996.
"This is something hard to describe, we carried the burden of the club's history of not being able to get a title and now we feel privileged, this moment is unforgettable for us," Tigres midfielder Damian Alvarez told reporters.
Santos were down to 10 men from the 13th minute after goalkeeper Oswaldo Sanchez was sent off for bringing down Brazilian forward Danilinho.
However, Tigres did not take immediate advantage as reserve keeper Miguel Becerra saved Lucas Lobos' penalty and then Santos leveled the tie at 1-1 on aggregate on the half-hour when striker Oribe Peralta scored from a Jose Cardenas pass.
Tigres equalised seven minutes into the second half when striker Hector Mancilla headed home a cross from Jorge Torres Nilo.
The home side's numerical advantage began to tell and in the 64th minute they went ahead with a goal by Danilinho.
Santos' frustration boiled over and centre-back Felipe Baloy was sent off for a bad foul on Lobos with 20 minutes left. Tigres also had defender Israel Jimenez red carded for trying to strike an opponent.
Substitute striker Alan Pulido put the match beyond doubt with Tigres' third goal four minutes from time following a one-two with Danilinho.
"We're going to rest for a few days because next week we're going to have to get working again," said Tigres coach Ricardo Ferretti after his 800th match as a trainer in Mexico.
The Clausura, the second of the season's championships, kicks off on January 6.
