Sentiment in Asian markets also got a lift on upbeat economic data from Europe and reassuring comments from a Federal Reserve official lifted Wall Street shares at the end of last week.
St. Louis Fed President James Bullard said on Friday that that the central bank's aggressive easy money policy will stay in place for a "long time." The comments helped push the Dow Jones stock index higher, although other major U.S. stock indices closed Friday in the red.
Adding to the upward momentum Friday was news that German business sentiment jumped at its fastest rate since July 2010 in February.
South Korean stocks bucked the regional trend and ended Monday almost 0.5 percent lower on concerns that the prospect of a more aggressive monetary policy in Japan will spell further weakness for the yen at the expense of the South Korean won.
In fact, the yen fell to its weakest level against the South Korean won since late 2008, with the strength in the won helping send shares in auto parts supplier Hyundai Mobis down more than 2.5 percent.
South Korean and Japanese firms compete against each other in a range of products from cars to TVs and computer chips.
The nation's new president Park Geun-hye was sworn in as the country's first female president Monday.
In Hong Kong, property-related stocks came under pressure following measures unveiled late on Friday to cool house prices. Hong Kong imposed higher stamp duties and home loan curbs, becoming the latest Asian country after China and Singapore to ramp up controls on the housing market this year.
Hong Kong property agent Midland Holding tumbled more than 5 percent, while property and construction was the worst performing sector on the Hang Seng Index. SHK shares fell almost 2 percent, while Cheung Kong, a leading local property developer, fell about 1 percent.
The losses in the property sector weighed on gains in the broader Hang Seng index, which closed up 0.2 percent higher.