Xie added that the controversial legislation will protect the law-based operation of international businesses in Hong Kong.

The "clouds of dust in Hong Kong have settled quicker than anyone had expected. Local risk sentiment isn't nearly as gnarly as everyone had feared," Stephen Innes, global market strategist at AxiCorp, wrote in a note on Tuesday.

There is also a sense of "re-opening optimism" among investors, said Innes. They are upbeat about lockdowns in the United States and elsewhere coming to an end.

In Japan, Prime Minister Shinzo Abe on Monday lifted the state of emergency for the entire nation, as the coronavirus outbreak there eases.

Abe is also eyeing a fresh stimulus package, saying that he would work to increase the government's stimulus packages to more than 200 trillion yen ($1.9 trillion), or about 40% of the annual output of the world's third biggest economy.

Dow futures are up more than 330 points. S&P futures rose nearly 1.4% and Nasdaq futures are up about 1.5%.