"It has been my dream all my life," De la Torre told a news conference on accepting the post, which he will begin once his club Toluca have completed their campaign in the Apertura championship that ends in December.
"Once I've finished that commitment, I'll take charge of the national team," said the 44-year-old nicknamed Chepo.
Aguirre resigned in July after Mexico's second round defeat by Argentina at the 2010 World Cup finals in South Africa and the position has been occupied in an interim capacity by several coaches who presided over friendlies since then.
De la Torre was originally competing for the job with Monterrey's Victor Vucetich, who pulled out over the weekend citing family reasons.
The appointment comes amid a team crisis after the Mexican Football Federation (FMF) sanctioned 13 players for holding an unauthorised late-night party after a friendly last month.
At the height of the crisis, the players threatened to boycott team call-ups and De la Torre's brother Nestor resigned from the post of FMF national teams director.
'DISCIPLINE, ORDER'
He had suspended forward Carlos Vela and midfielder Efrain Juarez for six months for breaking team rules and another 11 players including World Cup captain Rafael Marquez were fined.
"Discipline and order are valued in all institutions. We will have to agree on order, discipline and what it means to be in a national select, to be an example in all aspects, every day, 24 hours a day and everywhere," De la Torre said.
He added that selection to the team was open to all players and he would call up "those in the best condition, with the best ability and who are committed to being in a national select with all that means."
De la Torre has had a short but successful coaching career, winning league titles in his first job as head coach with Guadalajara in the 2006 Apertura championship and again in his first season with Toluca, the 2008 Apertura.
Toluca are the reigning champions after winning another title in the 2009/10 season's "Bicentenario" Clausura championship this year.
Mexico will take part in two tournaments next year, the CONCACAF Gold Cup in June and as an invited team in the Copa America, the South American championship, in Argentina in July.
FMF general secretary Decio de Maria said Mexico would also play numerous friendlies next year, the first in the United States on February 9 against opponents yet to be decided.
