It is the first such operation to take place since tensions between Taiwan and China increased following a visit by US House Speaker Nancy Pelosi to Taiwan earlier this month.
The US and other Western navies have routinely sailed through the strait in recent years.
China reacted to Ms Pelosi's visit by holding military drills in the area.
On Sunday, Taiwan's defence ministry says it detected 23 Chinese aircraft and eight Chinese ships operating around Taiwan.
Among the detected aircraft, seven crossed the median line of the Taiwan Strait - an unofficial barrier between Taiwan and China.
Washington says its two guided-missile cruisers - the USS Antietam and the USS Chancellorsville - are demonstrating freedom of navigation through international waters.
Beijing views such actions as provocative and maintains that the island of Taiwan is an integral part of Chinese territory.
On Sunday, its military said it was monitoring the two vessels' progress, maintaining a high alert, and was ready to defeat any provocation, Reuters news agency reports.
The US Navy said in a statement that the transit through the Taiwan Strait demonstrated the "United States' commitment to a free and open Indo-Pacific".
"These ships transited through a corridor in the strait that is beyond the territorial sea of any coastal state," the statement added.
Taiwan's defence ministry said the ships were sailing in a southerly direction and that its forces were observing, but that "the situation was as normal".
Taiwan is self-ruled, but China sees it as a breakaway province with which it will eventually unite, with force if necessary.
Taiwan has become yet another flashpoint between Washington and Beijing in recent years, with the US walking a diplomatic tightrope on the issue.
The US abides by the "One China" policy - a cornerstone of the two countries' diplomatic relationship which recognises only one Chinese government - and has formal ties with Beijing and not Taiwan.
But it also maintains a "robust unofficial" relationship with the island. That includes selling weapons for Taiwan to defend itself.
China reacted to Ms Pelosi's visit by holding military drills in the area.
On Sunday, Taiwan's defence ministry says it detected 23 Chinese aircraft and eight Chinese ships operating around Taiwan.
Among the detected aircraft, seven crossed the median line of the Taiwan Strait - an unofficial barrier between Taiwan and China.
Washington says its two guided-missile cruisers - the USS Antietam and the USS Chancellorsville - are demonstrating freedom of navigation through international waters.
Beijing views such actions as provocative and maintains that the island of Taiwan is an integral part of Chinese territory.
On Sunday, its military said it was monitoring the two vessels' progress, maintaining a high alert, and was ready to defeat any provocation, Reuters news agency reports.
The US Navy said in a statement that the transit through the Taiwan Strait demonstrated the "United States' commitment to a free and open Indo-Pacific".
"These ships transited through a corridor in the strait that is beyond the territorial sea of any coastal state," the statement added.
Taiwan's defence ministry said the ships were sailing in a southerly direction and that its forces were observing, but that "the situation was as normal".
Taiwan is self-ruled, but China sees it as a breakaway province with which it will eventually unite, with force if necessary.
Taiwan has become yet another flashpoint between Washington and Beijing in recent years, with the US walking a diplomatic tightrope on the issue.
The US abides by the "One China" policy - a cornerstone of the two countries' diplomatic relationship which recognises only one Chinese government - and has formal ties with Beijing and not Taiwan.
But it also maintains a "robust unofficial" relationship with the island. That includes selling weapons for Taiwan to defend itself.