Orders, a key indicator for the island's export-reliant economy, jumped 13.4 percent year-on-year to $44.91 billion, according to the economic affairs ministry.
Orders for information and mobile devices surged 21 percent from a year ago to a record $12.9 billion, thanks to brisk sales of new mobile devices, the ministry said.
The ministry did not identify the brands but the state-funded Central News Agency said strong demand for the iPhone 6 continued to boost export orders.
Apple said last month it sold 39.3 million iPhones in the three months ending September 27, up 16 percent from the same period a year earlier.
Taiwan's Hon Hai, also known as Foxconn, is the world's largest computer components manufacturer and assembles products for leading international brands including Apple's iPhones.
Media reports say local firms Pegatron Corp worked on the assembly of the new iPhone and TSMC -- the world's biggest contract microchip maker -- manufactured its chips. Neither company has confirmed the contracts.
Export orders from the United States hit a record $12.43 billion in October, up 17.4 percent from a year ago while those from Europe jumped 29.9 percent also to a record high of $9.52 billion.
Orders from mainland China and Hong Kong, Taiwan's other major overseas markets, were up 3.0 percent on-year to $9.98 billion but fell 4.0 percent from the previous month.