"I'm very proud to be the coach of the Mexican national team," Eriksson told reporters in a mixture of Spanish and Portuguese. "I accepted because it's a big challenge. Our target is the World Cup and to try and do better than last time."
Eriksson, whose career included stints with four Italian clubs and Portugal's Benifica, added: "As a Swede and having worked in various countries, I have learned Italian, Portuguese and English ... and in the next three months, I will be speaking acceptable Spanish."
Under Eriksson, England qualified for the 2002 and 2006 World Cups, but exited in the quarterfinals of each. Mexico exited in the round of 16 at those tournaments.
Sanchez's demise was set after his inability to beat the USA during his 16-month stint and his failure to qualify Mexico's U-23 team for the 2008 Olympic Games.
After Sanchez's firing, Mexico was led on an interim basis by Jesus Ramirez, who guided Mexico to the 2005 U-17 World Cup title.
Ramirez will remain in charge for Mexico's two-leg preliminary round World Cup qualifiers against Belize this month.
Eriksson's appointment comes after a several high-profile Mexican players said they were against bringing in a European coach. And the Mexcian federation is likely to come under criticism from the press.
"Obviously, I don't have a deep knowledge of Mexican soccer but that is something I'm going to change quickly," said Eriksson. "Like any coach who changes country, I will have to work and that doesn't bother me."