It is the highest profile Chinese deal to be rejected by Washington since Donald Trump came to power.
Regulators overseeing foreign investments in the US had refused to support the takeover, the firms said.
The geopolitical environment had "changed considerably" since the merger was announced last year, they added.
'Disappointed'
The collapse is a blow to the ambitions of Alibaba's billionaire executive chairman Jack Ma, who had promised President Trump that he would create a million US jobs.
