In remarks at a White House Rose Garden ceremony Tuesday, the president announced Snow's resignation and thanked him for his service.
"The Treasury Secretary is the leading force on my economic team and chief spokesman for my economic policies," Bush said. "For the past three years, Treasury Secretary John Snow has shown strong leadership in carrying out these responsibilities."
"I appreciate his years of service to our country," he added.
In the latest turnover in his administration, Bush called Paulson a "superb addition to my Cabinet," one who comes from one of the most respected firms on Wall Street.
“Mr. President, if confirmed, I look forward to working with you, your administration, and the Congress to help keep the American economy strong and competitive,” Paulson said.
Snow’s departure comes after more than a year of rumors and speculation that he would leave when Bush began making changes to his White House staff earlier this year.
White House press secretary Tony Snow said Bush offered Paulson the job five days before the president answered reporters' questions about a possible departure, during a meeting between the two. Paulson's acceptance the next day, on May 21, was subject to a background check, Bush's spokesman said.
Snow, the former head of railroad giant CSX Corp. who has a Ph.D. in economics, has served as treasury secretary since February of 2003. Snow replaced Paul O'Neill, who resigned because of police disagreements with the White House.
‘It’s been a great honor,” Snow said. “I’ve looked forward for some time to returning to private life. I do so in a great sense of satisfaction in what has been accomplished over the last three years.”
Paulson, 60, is chairman of the global banking and investment firm where he has worked since the 1970s. He has served as chairman for more than eight years.
Snow has called Paulson "a very able executive, a friend of mine."
Goldman Sachs is well-known for producing public officials. Robert Rubin, one of Paulson's predecessors, served as treasury secretary in the Clinton administration, and Jon Corzine, another Goldman Sachs chairman, served as a U.S. senator from New Jersey and is now governor of that state.
Bush began shaking up his staff months ago when he replaced Andrew Card as his chief of staff with Joshua Bolten, a former Goldman Sachs executive who had worked with Paulson.
Card was the first to leave shortly before other members of Bush's staff departed. Political adviser Karl Rove, press secretary Scott McClellan and CIA chief Porter Goss stepped down over a few weeks.
Last year, the Goldman Sachs group said it paid Paulson $30 million in total compensation in 2004 — almost a 40 percent gain from the year before.
The administration hopes that Wall Street executive can make a better case to promote Bush's positive economic accomplishments of low unemployment and growth. In the Rose Garden announcement, Bush noted that the U.S. economy grew last quarter at an annual rate of 5.3 percent, the unemployment rate is at a low 4.7 percent, productivity is high and wages grew at an annual rate of 5.7 percent in the first quarter of this year.
"The American economy is powerful, productive and prosperous, and I look forward to working with Hank Paulson to keep it that way. As treasury secretary, Hank will be my principal adviser on the broad range of domestic and international economic issues that affect the well-being of all Americans," Bush said.
Federal Reserve Chairman Ben Bernanke praised Snow for his "years of dedicated and able service" and said that he looked forward to working with Paulson, described by Bernanke as "highly respected throughout the financial world," according to a statement.
Sen. Charles Schumer, a Democratic member of the Senate Finance and Banking Committee that will hold Paulson's confirmation hearing, said he spoke with Paulson and offered support for his nomination.
"His experience, intelligence and deep understanding of national and global economic issues make him the best pick America could have hoped for," Schumer said in a written statement.
Senate Majority Leader Bill Frist issued a statement of support for Paulson.
“I know Mr. Paulson well and believe he is an excellent choice to take the helm of the Treasury Department,” Frist said. “The president and the economy will benefit greatly from his hands on experience in financial markets and understanding of business, investing and economic growth.”
Paulson departs Goldman Sachs as its stock trades at historic highs. Lloyd C. Blankfein will replace Paulson.
Robert Rubin, one of Paulson's predecessors, served as Treasury secretary in the Clinton administration, and Jon Corzine, another Goldman Sachs chairman, served as a U.S. senator from New Jersey and is now governor of that state.
Paulson was known on Wall Street for his dedicated support of environmental causes. Earlier this year, he made a gift of $100 million in Goldman stock to a family foundation dedicated to conservation and environmental education. Even after that gift, Paulson has a net worth estimated at more than $500 million.
Paulson, who was known to favor bird-watching in New York's Central Park to playing golf, is chairman of the Nature Conservancy and the chairman emeritus of the Peregrine Fund.
Last year, Goldman Sachs donated 680,000 acres in Chile to the Wildlife Conservation Society.
Snow has pushed President Bush's economic policies, promoting Social Security reform and an overhaul of the tax code. But his standing suffered as both proposals stalled.
"John answered the call to public service at a time of uncertainty for our economy. Under his leadership, we've seen a broad and vigorous economic resurgence," Bush said. "He's been a steady advocate for small business entrepreneurs and working families and he's helped deliver jobs and opportunity for the American people."
Financial disclosure forms have put Snow's estimated worth at between $43 million and $128 million. Two years ago he acknowledged an error of more than $10 million in his investment portfolio that caused him to lose nearly half a million dollars.
FOX News' Greg Kelly and The Associated Press contributed to this report.