As the House of Representatives approved the bill, which avoids tax hikes for most Americans and delays automatic spending cuts, investors piled into the embattled euro as risk appetite increased and oil prices surged.
Hong Kong was the biggest riser in Asia, up 2.19 percent at a 19-month high, receiving an additional boost from positive Chinese manufacturing data. Sydney gained 1.23 percent, or 57 points, to 4,705.9, and Seoul rose 1.76 percent.
Financial markets in Japan and mainland China were closed for a public holiday.
Asian shares had risen on Wednesday morning in anticipation of a deal in Washington, strengthening further after it was approved by US lawmakers.
Jason Hughes, head of premium client management for IG Markets Singapore, said the market reaction was "very positive".
"With the final hurdle being passed now, we've got a minimum deal that avoids any immediate threat of the US falling off the cliff... that's definitely boosted Asian equities markets," he said.
The gains followed jumps in US stocks on New Year's Eve as Congress moved towards a deal.
The Dow Jones Industrial Average finished up 1.28 percent, the S&P 500 gained 1.69 percent and the tech-rich Nasdaq Composite surged 2.00 percent.
The upbeat start for shares in 2013 will be a relief for investors after the uncertainty that clouded markets in the final months of last year as wrangling over the fiscal cliff dragged on.
The US deal passed the Senate early on Tuesday but its fate hung in the balance for hours as House conservatives sought to amend it to include big spending cuts, which would likely have killed it.
In the end, the House voted by 257 votes to 167 to pass the original bill after a bitterly contested session on New Year's Day.
The deal between the White House and Senate Republicans raises taxes on the rich and puts off automatic $109 billion budget cuts for two months.
Had it splintered, all Americans would have been hit by tax increases and spending cuts would have kicked in across the government, in a combined $500 billion shock that could have rocked the fragile recovery.
The House vote took place after a conservative rebellion fizzled when it became clear there were not sufficient votes in the restive Republican caucus to send an amended version of the bill with spending cuts back to the Senate.
Republican party leaders ultimately feared they would carry the can if the deal collapsed.
Hong Kong's Hang Seng Index was boosted by official data showing that Chinese manufacturing activity expanded in December for a third straight month, further evidence the world's number two economy was picking up after a slowdown.
The official purchasing managers' index (PMI) stood at 50.6 in December, unchanged from the previous month. A reading above 50 indicates expansion while anything below points to contraction.
The data was released on Tuesday, but the Hong Kong market had been closed for a public holiday.
On currency markets in Asian afternoon trade, the euro strengthened to $1.3258 from $1.3192 on Monday. The euro was at 115.51 yen from 114.45 yen.
The dollar rose to 87.12 yen from 86.69 yen but weakened against most other Asia-Pacific currencies.
On oil markets, New York's main contract, light sweet crude for delivery in February, added 84 cents to $92.66 a barrel in the afternoon and Brent North Sea crude for February delivery gained 66 cents to $111.77.
Gold was at $1,680.00 at 0545 GMT compared with $1,658.90 late Friday.
In other markets:
-- Taipei was up 1.04 percent, or 79.72 points, at 7,779.22.
Taiwan Semiconductor Manufacturing Co added 2.68 percent to Tw$99.6 while leading smartphone maker HTC was 0.83 percent higher at Tw$303.0.
-- Wellington was closed for a public holiday.