The deal is for 108 Abrams tanks, 250 Stinger missiles and related equipment.
Last month, China’s Foreign Ministry had urged the US to halt the sale, calling it an “extremely sensitive and damaging” decision.
China regards Taiwan as part of its territory which should be reunited with the mainland, by force if necessary.
Chinese foreign ministry spokesman Geng Shuang also called for the US to abide by the One China policy – under which the US recognises and has only formal ties with China and not Taiwan.
The sale of the weapons would not alter the basic military balance in the region, the Pentagon’s Defense Security Cooperation Agency (DSCA) said in a statement.
The DSCA has notified congress of the possible arms sale.
Taiwan’s Presidential Office expressed “sincere gratitude” to the US – which is the main arms supplier to Taiwan.
A spokesman for Taiwan’s president said in a statement to Reuters news agency that the island would “continue to deepen security ties with the US”.