China, which claims self-governed Taiwan as its own, routinely objects to US arms sales, adding to existing Sino-US tensions.
A statement from the US Defence Security Cooperation Agency said it had delivered the required certification notifying Congress following State Department approval for the sale, which was requested by Taiwan's de facto embassy in Washington.
Upgrades to the Patriot Air Defence System would "help improve the security of the recipient and assist in maintaining political stability, military balance, economic and progress in the region," the DSCA said in a statement.
The main contractors would be Raytheon Technologies and Lockheed Martin, it said.
Taiwan's Foreign Ministry said it "highly welcomed" the decision.
"In the face of China's continued military expansion and provocative actions, our country will maintain its national security with a solid defence, and continue to deepen the close security partnership between Taiwan and the United States," it said in a statement.
In Beijing, Chinese Foreign Ministry spokesperson Zhao Lijian offered strong condemnation.
"China will take appropriate and forceful measures to firmly safeguard its sovereignty and security interests," he told reporters.
Asked what measures China would take, Zhao said: "I wish to ask everyone to wait and see".
China has imposed sanctions on Lockheed Martin and other US companies in the past for selling weapons to Taiwan, though it is unclear what form the penalties have taken.
Taiwan's Defence Ministry has said the decision to obtain newer Patriot missiles was made during a 2019 meeting with US officials in the administration of President Donald Trump.
The ministry said the deal was expected to "come into effect" within one month.
The democratically governed island has complained of repeated missions by China's air force in its air defence zone, part of what Washington sees as Beijing's effort to pressure Taipei into accepting its sovereignty.
The United States, like most countries, does not have official relations with Taiwan, but Washington is its biggest backer and is bound by law to provide it with means to defend itself.
