Up to chest-deep floods were reported in some of the affected areas, including the capital of metro Manila, forcing authorities to suspend school classes and government work on Monday.
The national disaster agency and local officials say the fatalities were a 17-year-old girl and a 26-year-old woman who were buried in separate landslides in Cebu City, about 570km south of Manila.
Ten people were also injured from the landslides, the reports added.
Several domestic flights were cancelled, while sea travel was suspended in eastern and central ports, leaving more than 2200 passengers stranded, according to the coastguard.
The weather bureau said Yagi was packing maximum sustained winds of 75km/h and gusts of up to 90km/h.
It was moving west-northwestward at 15 km/h and was forecast to intensify into a severe tropical storm by Wednesday.
"It may also reach a peak category of typhoon by Thursday or Friday," the weather bureau added.
The Philippines is hit by an average of 20 tropical cyclones every year.
The strongest typhoon to ever hit the Philippines was Super Typhoon Haiyan, which killed 6,300 people and displaced more than four million in November 2013.
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