More than half a million people have fled coastal villages in the area, which was still recovering from Typhoon Haiyan last year.
In Tacloban, where thousands were killed by Haiyan, roofs have been blown away and streets are flooded. But Hagiput does not appear to have been as severe as many had feared.
So far there have been no reports of casualties, informs Report citing BBCNews.
The BBC's Jonathan Head in Legazpi, about 200km (125 miles) north of Tacloban, said Hagiput was clearly a powerful storm but nowhere near as powerful as Haiyan.
The authorities believed they were well prepared this time, he adds, but it could be some time before the extent of damage in more remote areas becomes clear.
Officials told the BBC that lighter than expected rain meant there was less chance of landslides, but that the strong winds could still bring down trees on homes.