The stocky former national team defender's appointment, a foregone conclusion after his success in the play-off, was announced after a Mexican Football Federation board meeting on Monday.
"In the meeting, the proposal was put forward for Miguel Herrera as national team coach with the appointment of Ricardo Pelaez as sporting director," national teams general manager Hector Gonzalez Inarritu said.
Herrera, whose previous appointment in mid-October was only for the two-leg play-off, will take up the job at the end of the Mexican Apertura championship on December 15.
Mexican daily El Universal reported on its sports website that the FMF planned to have Herrera stay on until the 2018 World Cup in Russia.
It quoted Gonzalez Inarritu as saying: "We want a good preparation for the World Cup. You know the contracts are without an end date, we like continuity."
Mexico fired Jose Manuel de la Torre in September following a loss to Honduras, and his successor, Fernando Tena, stepped down after a defeat to the United States in their next qualifier.
Victor Vucetich took over for the final two group games before being replaced by Herrera.
Herrera's club America, the defending champions, reached the semi-finals with a 1-1 draw at their Azteca home against UANL Tigres on Sunday. America went through on the away goals rule having drawn 2-2 at UANL in the first leg and will meet Toluca.
The 45-year-old, known affectionately as Piojo (louse), a nickname common in Latin America for a small boy or man, took charge after Mexico came within minutes of missing out on the World Cup finals for the first time since 1990.
Mexico, a traditional powerhouse in the CONCACAF (Confederation of North and Central America and the Caribbean), had underperformed in the region's six-nation final qualifying group.
Three coaches were sacked as Mexico's hopes of reaching Brazil faded with poor results, especially at the Azteca.
The top three teams - United States, Costa Rica and Honduras - booked automatic berths while Mexico and Panama were vying for fourth spot and the intercontinental play-off.
On the final day, Mexico were in fourth place, three points ahead of Panama, who had the better goals record.
Mexico lost 2-1 at Costa Rica, meaning a Panama victory at home to the United States would have sent them through to the finals for the first time.
Panama led the United States 2-1 going into added time only to concede two goals in less than three minutes and lose 3-2, allowing Mexico to secure fourth place and enter the play-off against Oceania winners New Zealand.
Vucetich, in charge for the last two games, was sacked and Herrera appointed.
He overlooked Mexico's top European-based players such as striker Javier Hernandez of Manchester United and Giovani Dos Santos of Villarreal and instead picked a home-based squad.
His team beat New Zealand 5-1 at the Azteca and won the return leg 4-2 in Wellington.
Mexico will find out their World Cup group rivals in Friday's draw in Brazil.
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