The Nikkei 225 index at the Tokyo Stock Exchange was up 178.61 points at 11,564.55 at the start.
The Nikkei and other newspapers said Japanese prime minister Shinzo Abe's cabinet had decided to nominate Kuroda as Japan's next central bank governor.
"Kuroda's reported selection is unquestionably a positive for stocks, as reflected in the yen's reaction," SMBC Nikko Securities general manager of equities Hiroichi Nishi told Dow Jones Newswires.
Mr Nishi noted that Mr Kuroda is well-connected and a supporter of the Japanese prime minister's monetary easing goals.
The dollar rose to 94.20 yen in early Asian trade on Monday from 93.37 yen in New York late Friday.
The euro changed hands at $1.3186 and 124.19 yen early Monday compared with $1.3189 and 123.18 in New York.
On Friday, the Dow Jones industrial average jumped 119.95, or 0.86 per cent, to 14,000.57 on renewed confidence that the US Federal Reserve stimulus programme would continue.
Stocks also got a lift from a bullish report on German business sentiment and from an earnings report from Dow member Hewlett-Packard, which surged 12.3 per cent.