The voyage risks further raising tensions with China but will likely be viewed by self-ruled Taiwan as a sign of support from the Trump administration amid growing friction between Taipei and Beijing.
Taiwan is one of a growing number of flashpoints in the US-China relationship, which also include a trade war, US sanctions and China's increasingly muscular military posture in the South China Sea, where the United States also conducts freedom-of-navigation patrols.
The two destroyers were identified as the William P. Lawrence and Stethem. The 112-mile-wide (180-km) Taiwan Strait separates Taiwan from China.
"The ships' transit through the Taiwan Strait demonstrates the US commitment to a free and open Indo-Pacific," Commander Clay Doss, a spokesman for the US Navy's Seventh Fleet, said in a statement.
Doss said there were no unsafe or unprofessional interactions with other countries' vessels during the transit.
Taiwan's Defense Ministry said the US ships had sailed north through the strait.
"US ships freely passing through the Taiwan Strait is part of the mission of carrying out the Indo-Pacific strategy," it said in a statement.
Taiwan's armed forces monitored the transit and nothing out of the ordinary happened during it, the ministry said.
There was no immediate comment from China.
The United States has no formal ties with Taiwan but is bound by law to help provide the island with the means to defend itself and is its main source of arms.
The Pentagon says Washington has sold Taipei more than $15 billion in weaponry since 2010.
China has been ramping up pressure to assert its sovereignty over the island, which it considers a wayward province of "one China" and sacred Chinese territory.
It said a recent Taiwan Strait passage by a French warship, first reported by Reuters on Wednesday, was "illegal."
Beijing's concerns about Taiwan are likely to factor strongly into this year's Chinese defense budget, following a stern New Year's speech from President Xi Jinping, threatening to attack Taiwan should it not accept Chinese rule.China has repeatedly sent military aircraft and ships to circle the island on drills in the past few years and worked to isolate it internationally, whittling down its few remaining diplomatic allies.