Investors spent the previous day worried about possible North Korean retaliation against South Korean military drills on a frontline island that was shelled by the North last month.
Instead, Pyongyang backed off threats to strike back and reportedly offered concessions on its nuclear program.
Japan's Nikkei 225 stock average rose 0.7 percent to 10,284.90 ahead of a policy decision by the central bank.
The Bank of Japan is expected to keep monetary policy unchanged at the current super loose setting after a key survey last week showed deteriorating business sentiment.
South Korea's Kospi advanced 0.7 percent to 2,034.70 and Australia's S&P/ASX 200 was up 0.7 percent at 4,769.3. Benchmarks in mainland China, Taiwan and New Zealand also rose.
In New York Monday, low trading volumes and a lack of economic reports kept stocks confined to a narrow range Monday. Indexes finished mixed and bond yields were barely changed.
The Dow Jones industrial average fell 13.78, or 0.1 percent, to 11,478.13. The broader Standard and Poor's 500-stock index rose 3.17, or 0.3 percent, to 1,247.08. The Nasdaq composite index gained 6.59, or 0.3 percent, to finish at 2,649.56.
In currencies, the dollar slipped to 83.69 yen from 83.78 yen late Monday. The euro rose to $1.3183 from $1.3126.
Benchmark oil for February delivery rose 37 cents at $89.74 a barrel in electronic trading on the New York Mercantile Exchange. The contract rose 77 cents to settle at $89.37 on Monday.