Both the dollar and the euro extended their gains on the yen, with the single currency hitting a five-year high in what should be a boost to Japanese exports, profits and stocks.
A Reuters poll found confidence at Japanese manufacturers rose for a second month to a three-year high in December, adding to the evidence of steady recovery in the world's third-largest economy.
The Nikkei share index jumped 1.8 percent and was fast approaching last week's peak at 15,794. South Korean stocks added 1 percent and MSCI's broadest index of Asia-Pacific shares outside Japan .MIAPJ0000PUS gained 0.2 percent.
While Friday's solid U.S. jobs report may have brought forward the day when the Federal Reserve starts tapering its asset buying, the figures also suggested the economy was recovering well enough to withstand the move.
A total of 203,000 jobs were added in November, while the unemployment rate dropped three-tenths of a percentage point to a five-year low of 7 percent.
"Markets are trading like they were well positioned for strong data, and would actually be relieved if the Fed tapers in December and so removes the tapering timing uncertainty," said Alan Ruskin, global head of FX strategy at Deutsche Bank in New York.
"That equities are this strong is a clear signal to the Fed that tapering will not do too much damage to risk appetite."
On Wall Street, the Dow Jones industrial average ended Friday with a gain of 1.26 percent, while the S&P 500 put on 1.12 percent.
Treasuries also proved resilient, with 10-year yields settling back at 2.86 percent after a brief spike to 2.93 percent immediately after the jobs report.
The Fed has also had some success in convincing investors that tapering is not tightening, and that interest rates will remain low for a long time to come.
Fed funds futures are not fully priced for a hike until the very end of 2015, while yields on two-year Treasuries have held around 30 basis points for weeks now.
The improvement in risk appetite knocked safe havens like the yen, lifting the U.S. dollar to 103.07 yen early Monday and near last week's highs around 103.37.
The euro had shot up to 141.29 yen, territory not visited since October 2008, while also making ground on the U.S. dollar. It briefly touched $1.3747 early on Monday before edging back to $1.3705.
The common currency has been underpinned by rising short-term interest rates after the European Central Bank dampened hopes for an imminent easing move.
Aiding sentiment in Asia was a set of robust trade numbers from regional powerhouse China. China's exports came in well above forecasts in November, rising 12.7 percent from a year earlier, while imports rose 5.3 percent.
"The strength is likely supported by the recent improvement in global manufacturing activity, as evidenced by the strong PMI prints in major advanced economies," wrote analysts at Barclays in a note.
That should be positive for many commodities with China importing a record amount of iron ore in November, while oil imports rebounded.
Prices for the steel-making mineral have been surprisingly firm around $139 a tonne recently, good news for Australia as it is the country's single biggest export earner.
That helped the Australian dollar nudge ahead to $0.9105 early Monday, well up from Friday's lows around $0.8989.
U.S. crude oil futures were trading 4 cents firmer at $97.69, having surged more than 5 percent last week. Brent edged up 2 cents to $111.63 a barrel.
Gold has not been so fortunate, with the metal stuck at $1,227.46 and only just above five-month lows.