Eriksson signed a six-month deal and will lead the team at its first Asian Cup in January and February, alongside Irishman Scott Cooper, BBC Sport reported.
It is the 70-year-old Swede's first job in management since being sacked by Chinese side Shenzhen in June 2017.
Ex-England captain Terry Butcher quit as Philippines head coach in August before he had taken charge of a match.
"With his reputation, experience and knowledge, there's no question he can help the team reach the next level," Philippines general manager Dan Palami said of Eriksson, who was in charge of England from 2001 to 2006.
He held talks about becoming Cameroon manager in July, and was in charge of the Ivory Coast for three months in 2010, including at the World Cup in South Africa.
"There were a lot of countries and clubs interested in Sven's services, but we were able to sell him the idea of leaving a legacy here in the Philippines." added Palami.
Cooper, who worked with Eriksson at Leicester City, has been in charge of first-team affairs since Butcher's departure.
Before the Asian Cup next year, the Azkals take part in the AFF Championship in November and December.