Chinese authorities reported the lowest daily rise in new virus cases since Jan. 29 on Wednesday, as the number of new infections fell for a second straight day.
The mood was also lifted by expectations that China - the region's biggest trading partner - would lower its benchmark loan prime rate on Thursday.
Philippine stocks gained 1%, the most in the two weeks, and led gains in the region. Conglomerates SM Investments and Ayala Land firmed more than 2.5% each.
The Indonesian benchmark rose for the third straight session, supported by financials. Lender PT Bank Mandiri (Persero) Tbk added 1.6%.
Bank Indonesia is also set to cut interest rates on Thursday, according to a slim majority of analysts polled by Reuters.
"Asia seems confident that the region's governments will 'do what it takes' to offset the coronavirus slowdown," Jeffrey Halley, an analyst at OANDA, said in a note.
Halley added that Singapore's "blockbuster budget stimulus" on Tuesday further added to hopes that other regions will follow suit.
The city-state had announced around $4.5 billion in financial packages to help contain the virus outbreak.
Singaporean equities ended a four-session losing streak, as index heavyweights United Overseas Bank and DBS Group Holdings rose 0.9% and 0.2%, respectively.
However, the Thai index erased early gains to close 0.5% lower, dragged down by utilities stocks.
Thailand's central bank said the country's economy will grow at a much slower pace than previously forecast this year and much further below its potential, in a minutes of meeting earlier this month when it cut interest rates to a record low.
In December, the bank had predicted growth of 2.8% for 2020, but recently said it might be less than 2%.
By Arundhati Dutta