The benchmark Nikkei 225 index jumped 1.78 percent, or 482.26 points, to end at 27,587.46, while the broader Topix index rose 1.60 percent, or 30.38 points, to 1,929.43.
The dollar fetched 147.92 yen, from 147.46 yen in New York on Friday.
Wall Street tech shares jumped, with Apple soaring nearly eight percent after reporting higher profits.
Stocks in New York and worldwide have also enjoyed a boost in recent days on optimism that the Federal Reserve will soon moderate its aggressive policies to counter inflation.
“It’s a good period for people who want to buy Japanese shares with a long-term outlook, but the market could move up and down short-term,” said chief strategist Masayuki Kubota of Rakuten Securities.
The cheap yen and expectations related to the reopening of the economy after the pandemic, including the resumption of tourism, are also positive factors for the market, Kubota added.
Traders are watching financial results from Japanese corporations, which will be in full swing from Tuesday, when Toyota and Sony release their reports.
Japan’s factory output in September, released on Monday morning, fell 1.6 percent on-month, the first drop in four months.
The government however maintained its basic assessment that output is “showing signs of picking up moderately”.
SoftBank Group soared 6.20 percent to 6,400 yen while Uniqlo operator Fast Retailing climbed 0.89 percent to 82,990 yen.
Automakers were higher, with Toyota advancing 1.45 percent to 2,059.5 yen, Nissan jumping 2.81 percent to 474.4 yen and Honda rising 1.62 percent to 3,373 yen.
ANA Holdings, which owns Japan’s biggest airline ANA, firmed 1.03 percent to 2,891 yen.
After the closing bell, the company revised up its full-year net profit forecast to 40 billion yen from the previous estimate of 21 billion yen, citing a recovery in demand following the recent easing of Japan’s border restrictions.