In a White House announcement, George Bush praised Paulson's lifetime of business experience and said he had the ability to explain complicated economic concepts in clear language.
The president said Paulson would be pursuing long-standing White House economic policies.
Naming Paulson gives Bush a Wall Street heavyweight to use as an advocate for his tax-cut policies, which he calls an important factor in the growing economy, but which his opponents say have contributed to long-term budget deficits.
"He will work closely with the Congress to restrain the spending appetite of the federal government and keep us on track to meet our goal of cutting the deficit in half by 2009," he said.
In addition, he said Paulson will be an important representative of the US in trying to open markets for US goods.
"He will insist on fair treatment for American businesses, workers and farmers. He will help ensure that our trading partners play by the rules, respect international property rights and maintain flexible market-based exchange rates for their currencies," Bush said.
Another item on Paulson's agenda will be expanding trade and persuading China to move quickly to a market-based exchange rate as a way to help US goods be more competitive in China.
"He will insist on fair treatment for American businesses, workers and farmers"
George Bush, the US president
Snow's resignation - long rumoured about - comes at a time when the US economy is moving along briskly, although with hints of inflation on the horizon.
Paulson said that in his 32-year career in finance, he has developed an appreciation of the role that capital markets play in driving economic growth and efficiency.
"Our economy's strength is rooted in the entrepreneurial spirit and the competitive zeal of the American people and in our free and open market," he said.
Paulson must be confirmed by the Senate.
CIA chief sworn in
Also on Tuesday, General Michael Hayden was sworn in as CIA director.
Hayden told the officers at the embattled agency that they must be competent and co-operative to keep the "central" in Central Intelligence Agency.
Hayden (R) urged officers to keep
the 'central' in CIA
Even with those marching orders, Hayden reassured the agency that it remains crucial to US spy operations and analysis.
In his first day on the job, Hayden told his staff that only the CIA has the "connective tissue" to bring the intelligence community together.
Hayden, the former NSA chief who served as the country's No. 2 intelligence official for the last year, was sworn-in by his boss John Negroponte, the national intelligence director.
At his confirmation hearing this month, Hayden said he wanted the CIA to focus on traditional spycraft and reward risks taken by operatives in the agency's clandestine service.
He also said he wanted CIA analysts to be clear in their language when they are unsure of judgments but to be unafraid of hard-edged assessments.