Fernando Basualdo, head of the German-company Adidas in Mexico, refused to reveal the contract's worth. Mexican newspapers estimated it at between US$70 million and US$88 million (€55 million and €70 million).
Nike had sponsored the teams for the last four years.
However, Nike received poor publicity in August when its officials made members of the returning Mexico under-20 women's team at Mexico City airport hand over their Nike sports bags for the senior women's team.
Mexican Football Federation general secretary Decio de Maria said the incident was not the reason the federation switched sponsors. Adidas made a better bid and had good designs, he said.
Adidas will provide uniforms for both the male and female teams in all age groups.
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