The chamber approved the nomination in a voice vote. The action came just hours after the nomination won the endorsement of the Senate Finance Committee, which oversees the Treasury Department.
Paulson, a 32-year Wall Street veteran, is the chairman and chief executive officer of Goldman Sachs Group Inc., a financial powerhouse.
Both Democrats and Republicans welcomed Paulson's nomination.
"I am convinced he is the right man at the right time," said Sen. Ron Wyden, D-Ore., before Thursday's vote.
Sen. Kit Bond, R-Mo., called Paulson a "very strong choice for Treasury secretary."
Beset by low job approval ratings, Bush is looking to Paulson to help energize the administration's stalled second-term economic agenda. The nomination was part of a flurry of other changes in the president's personnel lineup.
During a nearly three-hour hearing on his nomination on Tuesday, Paulson, 60, hewed closely to the Bush administration's stance on a wide range of economic policies.
For instance, although he thought it was wise to trim the federal budget deficit, he said it would be a mistake to raise taxes to help fix the problem. He also said that he would focus on prodding China to revamp its currency policy, a practice critics blame for contributing to the United States' record-high trade deficit and to the loss of U.S. factory jobs.
He said he wanted to pursue efforts to crack down on abusive tax shelters, work on ways to collect billions in taxes owed to the U.S. government, and explore ways to simplify the tax code. He also promised to review a once-secret Treasury program that gave the government access to a data base of international banking information to catch suspected terrorist financiers.
Paulson will be President Bush's third treasury secretary and would succeed John Snow, who has held the post since February 2003. Snow had replaced Paul O'Neill, once a top executive at aluminum giant Alcoa.
As the president's top economic salesman, Paulson will take the Treasury helm at a challenging time for the economy with growth slowing and inflation rising.
Big budget and trade deficits pose risks for the economy. Trade tensions are running high with China. And, there's some anxiety over whether the value of the U.S. dollar will gradually and smoothly decline or whether there might be a dangerously jarring and steep descent.
A millionaire many times over, Paulson earned $35.06 million in salary from Goldman Sachs last year, an amount that included cash and stock options.
Paulson will sell his holdings in the Wall Street firm to comply with government conflict-of-interest rules, the White House said last week. He owns 3.23 million shares of stock, worth more than $470 million. His total net worth is estimated to be above $700 million.