Vucetich takes charge with Mexico in fifth position in the final round of CONCACAF qualification for the finals in Brazil next year.
After topping their group in the third phase, winning all six games, Mexico have endured a dismal last round thus far, winning only once and finding the net on just four occasions.
Friday's disappointing 2-1 home defeat to Honduras spelled the end of Jose Manuel de la Torre's reign, with Luis Fernando Tena taking temporary charge for the 2-0 loss to United States on Tuesday.
Vucetich possesses a wealth of experience, having managed at an array of clubs in Mexico, but parted company with Monterrey last month following a poor start to the new season.
The 58-year-old enjoyed great success with Monterrey, guiding them to two Apertura titles and three consecutive CONCACAF Champions League crowns from 2011 to 2013.
Mexico have been present at every World Cup since 1994, and last missed the finals in 1990, when they were banned for using players over the age limit in qualifying for the 1989 FIFA World Youth Championship.
However, Vucetich faces a difficult task if he is to ensure that Mexico reach the 2014 tournament, with their last home game coming against Panama, who occupy the intercontinental play-off spot on goals scored, on October 10.
Mexico travel to Costa Rica, who have already qualified for the World Cup, in their final qualifier on October 14.
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