The main cause for Nikkei cheer was a corporate failure
The benchmark Nikkei 255 share index closed up 5.8% - its biggest one-day percentage gain for a year - at 11,450.22 points.
The Nikkei, which has performed miserably over the past couple of years, has now risen by almost 20% in the past six weeks.
Investors hope that the government now has the political will to push through much-needed but unpalatable restructuring of debt-ridden Japanese firms.
Monday's rally was also fuelled by a positive performance on Friday in New York, where hi-tech shares have been performing particularly strongly.
Failure helps
Paradoxically, a major domestic factor underpinning the Nikkei on Monday was a corporate bankruptcy.
The failure of debt-ridden builder Sato Kogyo over the weekend was taken as a sign that banks are speeding up their disposals of bad loans.
This encouraged heavy buying of bank and other financial shares, which have long been some of the poorest performers on the Tokyo Stock Exchange.
Mizuho, the world's largest banking group by assets, jumped a whopping 14%.
Shares were also supported by tighter policing of the rules on short-selling, the practice of selling shares one does not own, in the hope that prices will go down.
Dismal past
The Tokyo stock market, one of the biggest in the world, has been a dismal performer for more than a decade.
It peaked at almost 38,000 points at the end of the 1980s, before starting a near-uninterrupted slide towards 10,000.
Aside from a rally in 1999-2000, the past few weeks' surge has been the only serious bull market since then.
The pessimism driving shares down was the result of economic gloom, as investors doubted the government's ability to reform its way out of the slump that took hold in the 1990s.
Japanese industry is heavily indebted, causing the country's vital banking sector to suffer from shabby balance sheets.
A succession of governments riven by factional infighting and pork-barrel politics have done little or nothing to shake up the systems underpinning the decline.
But this year, the government of Prime Minister Junichiro Koizumi has made increasingly convincing noises about tackling the slump, including a plan last week to fight debilitating deflation.
Mr Koizumi's popularity has been weakening since he sacked his popular - if abrasive - foreign minister, Makiko Tanaka, in a move seen as placating the anti-reform party old guard and bureaucracy.
But still the hope is that reforms will now gain pace.
Year-end looms
It is not clear, however, how long this rally will last.
The Japanese financial year closes at the end of March, and most expect the increase to continue until then at least.
But thereafter, there is little to keep the market supported, and most analysts predict that the government will have to inject cash into the banking system by the summer.