Japan's benchmark Nikkei 225 index closed up 1.22% at 19,630.63.
Shares in Japanese exporters were lifted as the dollar strengthened against the yen on expectations of a US interest rate rise in December.
A weaker yen is good for Japan's big exporters as it makes their products cheaper to buy overseas.
The dollar neared a one-week high in Asia trade at 123.39 yen, compared with 123.18 in New York.
In Australia, Sydney's benchmark S&P/ASX 200 index closed up 2.3% at 5,118.20.
After falling on Monday over worries about air travel following the Paris attacks, several airlines saw their shares recover on Tuesday.
Qantas shares closed up 5.29%, while Virgin Australia shares finished the day up 2.33%.
In China, Hong Kong's Hang Seng index closed up 1.15% at 22,264.25, while the Shanghai Composite lost earlier gains to close nearly flat, down 0.06%, at 3,604.80.
In South Korea, the benchmark Kospi index closed up 1.06% at 1,963.58.
Asian shares were higher following Wall Street's positive close, as global markets largely held firm despite Friday's terror attacks in Paris.