The TWSE jumped 127.71 to 5650.83, bringing gains this month to 6.3 percent. TWSE futures contract for September delivery advanced 2.2 percent to 5668.
The US economy grew at a 3.1 percent annual rate from April through June, the fastest since last year's third quarter, the US Commerce Department said. The increase was faster than last month's estimate of 2.4 percent, the department said.
The US is the second-biggest export market for Taiwan and Hong Kong after China.
Hong Kong's Hang Seng Index climbed 1.4 percent to 10,908.99.
The benchmark advanced 7.6 percent in August, its fifth month of gains and the longest winning streak since 1996. The September futures added 1.2 percent to 10,900.
Li & Fung, which buys Asian-made garments on behalf of Abercrombie & Fitch Co, climbed 3.1 percent to HK$13.25. Johnson Electric Holdings Ltd, the world's second-largest maker of small electric motors, rallied 5.7 percent to HK$12.15.
South Korea
In South Korea, the Kospi index added 0.9 percent to 759.47.
For the month, the benchmark rallied 6.4 percent. Kospi 200 futures for September climbed 0.7 percent to 97.60, while the underlying index gained 0.9 percent to 97.59.
Hyundai Motor, whose exports account for more than half of sales, advanced 3.7 percent to 39,200 won. Shares of the nation's largest automaker also rose after the company said it may buy back 2.5 percent of its shares from Mitsubishi Corp to stabilize the automaker's management.
LG Electronics Inc, South Korea's second-largest electronics maker whose exports account for more than 60 percent of sales, rose 2.9 percent to 64,000 won.
"The US economy is clearly picking up, sending exporters higher," said Kim Jae Ho, who helps manage the equivalent of US$254 million at Seoul Investment Trust Management Co.
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