"The proposed sale will help improve the security of the recipient and assist in maintaining political stability, military balance, and economic progress in the region," the agency, which oversees major arms sales, said.
US legislators have 30 days to block the six separate arms deals, although such action is rare since any major arms agreements are carefully vetted before they are made public.
Many of the weapons to be sold were part of a package announced by George Bush, the US president, shortly after he took office in 2001.
They were initially held up by partisan wrangling in Taiwan's legislature over paying for them.
The Pentagon said the arms sales were consistent with the Taiwan Relations Act, which obliges Washington to help Taipei defend itself.
The deals were announced after what analysts had described as a freeze designed to ease tension between Beijing and Taipei, and were quickly praised by Taiwan.
Taiwan's economic and cultural representative in the US said the decision marked the end of eight years of "turmoil and confusion" and heralded "the beginning of the new era of mutual trust between our two countries".
China has claimed sovereignty over Taiwan since 1949, when the Communists, led by Mao Zedong, won the Chinese civil war and the defeated Nationalists fled to the island.
Beijing has vowed in the past to bring Taiwan under its rule, by force if necessary.
The US switched diplomatic recognition from Taipei to Beijing in 1979, recognising "one China", but remains Taiwan's biggest ally.
The sales include 30 AH-64D Apache Longbow attack helicopters built by Boeing, along with night vision sensors, radar, air-to-air missiles and Hellfire missiles. That deal alone is worth $2.5bn, if all options are exercised.
In addition to Boeing, major contractors will include General Electric for engines, Lockheed Martin Corp, Northrop Grumman Corp, Raytheon Co and Britain's BAE Systems.
The Pentagon also approved the sale of Patriot advanced capability PAC-3 missiles, radar sets, ground stations and other equipment valued at up to $3.1bn. Raytheon would be the main contractor, along with Lockheed.
Omitted from the arms deal package were two items Taiwan had originally sought - diesel-powered submarines and 60 UH-60 Black Hawk helicopters, Rupert Hammond-Chambers, president of the US-Taiwan business council, said.