But Democratic hopes to add Clinton to that list were sidetracked when one senator, Republican John Cornyn of Texas, objected to the unanimous vote.
Cornyn said he still had concerns about foreign donations to the foundation headed by Clinton's husband, former President Bill Clinton.
Those confirmed were Steven Chu to be energy secretary, Arne Duncan at education, Janet Napolitano for homeland security, Eric Shinseki to head veterans affairs, Ken Salazar for interior and Tom Vilsack to lead the department of agriculture.
The Senate also approved Peter Orszag, recently the director of the Congressional Budget Office, to head the White House's Office of Management and Budget.
Obama signed nominating papers for his Cabinet choices about an hour after he took the oath.
Senate leaders agreed to have a roll call vote on Clinton on Wednesday after three hours of debate. Jim Manley, spokesman for Senate Majority Leader Harry Reid, predicted that "she will receive overwhelming bipartisan support at that time."
The Wednesday vote became necessary when Cornyn objected to the voice vote. In the Senate, a single senator can block measures from being approved by voice.
He said he wanted "a full and open debate and an up-or-down vote on Sen. Clinton's nomination." He said important questions remain unanswered concerning the foundation headed by former President Bill Clinton "and its acceptance of donations from foreign entities. Transparency transcends partisan politics and the American people deserve to know more."
Cornyn's spokesman Kevin McLaughlin said the senator is not trying to block her confirmation, but is seeking more debate about the donations.
Several Republicans raised questions at Clinton's confirmation hearing about possible conflicts of interest from Bill Clinton's fundraising work and his acceptance of large donations from foreign countries and companies.
Sen. Richard Lugar of Indiana, top Republican on the Foreign Relations Committee, urged Clinton to improve transparency in her husband's fundraising. He said the former president's foundation should stop taking foreign contributions while Clinton serves as secretary of state. McLaughlin said Cornyn has asked Clinton to take similar steps.
In her testimony, Clinton said the foundation would provide a clearer picture of its annual donations.
Also left unconfirmed were several other top members of Obama's cabinet. Timothy Geithner, the nominee to head the treasury department, faces the Finance Committee Wednesday, where he will have to explain his initial failure to pay payroll taxes he owed while working for the International Monetary Fund.
The Judiciary Committee is expected to vote as early as Wednesday on Eric Holder to be attorney general. Also still in the confirmation process is former Senate Democratic leader Tom Daschle, Obama's pick to head health and human services and spearhead his efforts to reform health care.
Robert Gates, who has served as defense secretary under President George W. Bush, will continue in that position in the Obama administration.
The Senate traditionally moves quickly to affirm the new president's Cabinet.
Eight years ago the Senate approved seven members of President George W. Bush's Cabinet, including Colin Powell to be secretary of state.
On Bill Clinton's first day in office in 1993, the Senate gave the go-ahead for the secretaries of state, defense and treasury. They next day it approved eight more Cabinet officers.
Of the new Cabinet secretaries, Chu is a Nobel Prize-winning physicist who has promoted alternative energy and warned of global warning as director of the Lawrence Berkeley National Laboratory in California.
Vilsack moves to agriculture after serving as governor of Iowa, one of the nation's leading farm states, while Napolitano is a two-term governor of Arizona, where such homeland security issues as illegal immigration and secure drivers' licenses have been prominent issues.
Salazar has served four years as senator from Colorado, where he took pro-environmental positions on such issues as drilling for oil in the Alaska National Wildlife Refuge.
Shinseki, as former Army chief of staff, gained national attention in 2003 when he told Congress, prior to the invasion of Iraq, that it would take several hundred thousand U.S. troops to control the country afterward. That differed with the opinions of some Bush administration Pentagon leaders, and he retired soon after.
Duncan has been superintendent of public schools in Obama's hometown of Chicago since 2001.