Japan's Nikkei 225 rose 1.3% to close at 16,960.16, extending the previous day's jump of more than 4%.
Electronics giant Toshiba finished 7.1% up on reports it had secured a further 250bn yen ($2.2bn; Â£1.6bn) in bank loans for its restructuring efforts.
The Japanese company is in the process of a major overhaul following a massive accounting scandal.
In China, the mainland Shanghai Composite index closed up 0.35% at 2,859.76, while Hong Kong's Hang Seng was one of the only indexes in the region that finished the day lower, down 0.3% at 19,941.76.
In Australia, the benchmark ASX/200 index finished the session up 1.2% at 5,081.10.
Commodity firms saw strong gains for a second day, with Rio Tinto and Fortescue rising 2.8% and 6.7% respectively.
Investors reacted positively to the settlement between Brazil and Samarco over the 2015 mudslide, which was caused when a mine breached a dam. The mudslide killed 19 people and caused widespread environmental damage.
Samarco is partly owned by Anglo-Australian mining giant BHP Billiton, which saw its shares rise 3.6%.
In South Korea, the Kospi index closed up 0.5% at 1,958.17.
After reporting strong car sales figures earlier in the week for the country's car makers in the US, Wednesday saw equally strong February data coming in for the domestic market.
The country's top car makers, Hyundai, Kia and Ssangyong, all saw gains throughout the day.
Asian shares traded mostly higher for a second day after Wednesday's strong rally across the region.