Farias, who replaces Argentine Sergio Almiron, will prepare Tijuana for the Clausura campaign, the second championship of the 2013/14 season, which kicks off in mid-January.
"Tijuana has officially signed Venezuelan trainer Cesar Alejandro Farias Acosta, who has been designated the club's coach as from the 2014 Clausura tournament," the border town club's management said in a statement.
"The South American coach will begin pre-season work with Tijuana on December 6," they added.
The 40-year-old Farias, who began coaching at local club level in the late 1990s, steered Venezuela to their best finish in the Copa America - the semi-finals in Argentina in 2011.
Venezuela, the only South American team never to have reached the World Cup finals, failed to make the 2014 tournament in Brazil, finishing sixth in the group, five points behind Uruguay who earned a place via an intercontinental playoff.
Tijuana's first division rivals Cruz Azul sacked coach Guillermo Vazquez on Tuesday after being eliminated by Toluca in the Apertura championship quarter-finals at the weekend.
Vazquez, 46, joined the Blue Machine in 2012 and led them to the final of last season's Clausura where they lost to America.
Three former Mexico coaches, Jose Manuel de la Torre, Luis Fernando Tena and Victor Vucetich, who were all sacked during a fraught campaign to qualify for next year's World Cup, are among the candidates to replace Vazquez.
Mexico finally managed to qualify for the tournament in Brazil under coach Miguel Herrera with a victory over New Zealand in last month's intercontinental playoffs.
Herrera was confirmed on Monday as Mexico coach for the finals and will take charge again later this month after the Apertura in which his club side America, who meet Toluca in the semi-finals, can win a record 12th, and their second straight, league title.
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