The Nikkei 225 index at the Tokyo Stock Exchange opened up 83.52 points to 8,371.01.
Optimism over a pact came even as the Organisation for Economic Co-operation and Development warned that the debt crisis could plunge advanced economies into deep recession and even depression.
US President Barack Obama told top European officials Monday to take decisive action on the region's fiscal woes, while ratings agency Moody's warned that all European states were at risk of seeing their credit ratings cut.
A swift improvement in the crisis was unlikely, despite hopes European leaders meeting in Brussels Tuesday will reach a workable deal to contain the problem, said Kenichi Hirano, operating officer at Tachibana Securities.
"The situation has to be watched closely for an extended period. The outlook, however, changes slightly day by day," Hirano told Dow Jones Newswires.
US stock markets jumped on Monday, boosted by suggestions that Europe's leaders may finally cobble together a plan to fix the continent's long-running debt crisis.
Markets also responded to data showing sales over the US Thanksgiving holiday weekend were up 16 percent from last year to a record $52.4 billion.
That marked the biggest dollar amount ever spent over the so-called Black Friday period, the unofficial start of the Christmas shopping season.
The Dow Jones Industrial Average gained 2.59 percent to reach 11,523.01.
The euro bought $1.3300 and 103.82 yen in early Asian trade, compared with $1.3318 and 103.83 yen in New York late Monday.
The dollar traded at 78.06 yen, marginally up from 77.97 yen.
Before the Tokyo market opened, the government released a raft of economic data, including a monthly labour report that showed Japan's jobless rate rose to a worse-than-expected 4.5 percent in October from 4.1 percent in the previous month.