In Europe, France's CAC-40 rose 0.4 percent to 4,307, while Germany's DAX rose 0.5 percent to 9,211. The FTSE 100 index of leading British shares was 0.3 percent higher at 6,713.
Futures indicated that U.S. stocks would open up, too. S&P 500 futures rose 0.1 percent, while Dow futures were up 0.2 percent.
Markets, particularly in Asia, have also been supported by China's announcements of more details to its economic and social reform program, including opening state industries to greater competition, loosening its one child policy, and abolishing its labor camps.
China's leadership has faced pressure to replace a worn out economic model after growth slowed to a two-decade low in the second quarter. The details were announced last Friday after Asian markets had closed so this was the first response local investors had to trade on the news.
"An easing of the one child policy and scope for extensive growth in the financial sector are the sort of factors that have helped drive equities across much of the region," analysts at Monex Capital Markets said in a note.
China's Shanghai Composite surged 2.9 percent to 2,197.22 and Hong Kong's Hang Seng jumped 2.7 percent to 23,660.06. South Korea's Kospi was up 0.3 percent to 2,010.81 but Tokyo's Nikkei 225 reversed early gains to close fractionally lower at 15,164.30.
Elsewhere, trading was fairly lackluster. Among currencies, the euro was up 0.1 percent at $1.3507 while the dollar fell 0.2 percent to 100.10 yen.
In energy markets, benchmark crude for December delivery was down 26 cents at $93.58 in electronic trading on the New York Mercantile Exchange.