Alvarez, commonly known as Vadao, will replace Lima at the helm after she became the first female to ever coach the women's national team.
Lima, who had been in charge of the six-time Copa America Femenina champions since November of last year, was sacked after a run of six straight matches without a win.
Of those six matches, three consecutive defeats came courtesy of the Matildas in their triumphant run at last month's Tournament of Nations and in international friendlies last week.
Australia thumped Brazil 6-1 to claim the inaugural Tournament of Nations trophy last month and added insult to injury by defeating them 2-1 in Sydney and 3-2 in Newcastle in their recent blockbuster friendlies.
The returning Alvarez meanwhile led Brazil to a gold medal at the 2015 Pan American Games but failed to medal at the 2016 Rio de Janeiro Olympics after losing to Sweden on penalties in the semi-finals.
Boasting five-time world player of the year Marta Vieira, Brazil will hope the respected 61-year-old will be the man to take them back to the top of women's football.