The move comes just hours after being released by the New York Red Bulls on Thursday morning.
Goal.com reported earlier this week that Marquez was in Mexico City to finalise the deal, but the one major hurdle in completing the move sooner was his contract obligations with the Red Bulls.
"I'm sure that our fans will give Leon's newest player, Rafael Marquez, the best welcome," Leon president Jesus Martinez wrote on Twitter.
Marquez, who was one of the Red Bulls' three Designated Players, (a player they can sign outside of the team's salary cap) had been a disappointment since joining the MLS team from Barcelona in 2010. He played just 35 of a possible 73 games while earning $4.6 million (€3.5m), the second-highest salary in MLS.
The Red Bulls' new sporting director Andy Roxburgh said it was a mutual decision to part ways with Marquez.
“This decision has been made in the best interests of both parties concerned,” Roxburgh said. “Rafa has accomplished a great deal during his career and is a top quality player. We want to thank him for his service to the Red Bulls and wish him the best of luck in the next stage of his career.”
Marquez began his career in Mexico with Atlas before playing in Europe with Monaco and Barcelona. He also has 106 caps with Mexico.