The decision closed a rancorous session in which Republicans first sought to push Bolton through the Foreign Relations Committee and Democrats resisted.
"We'll all have to trust each other," said Sen. Richard Lugar, R-Ind., the committee chairman, in sealing the unanimous agreement.
Republicans hold a 10-8 majority on the panel, and Lugar had sounded confident early in the session that he had the votes to prevail.
But Republican Sens. Chuck Hagel of Nebraska and George Voinovich of Ohio, both expressed reservations about a quick vote — as did a solid phalanx of Democrats.
"Although the committee began with the chairman, Senator Richard Lugar saying that the vote was clear on the committee, the only thing clear at the close of the session was that allegations were becoming more numerous and the old adage, 'It's not over until it's over,' was the rule of the day," reports CBS Foreign Affairs Analyst Pamela Falk.
Bolton is a harsh critic of the United Nations bureaucracy and thus was a provocative choice to be the administration's representative to the world body.
That was enough to generate some Democratic opposition, and his troubles were compounded by allegations about his temperament and his ways of dealing with subordinates.
President Bush has no second thoughts about Bolton as his choice to be United Nations ambassador, the White House said Tuesday, despite critics' complaints about Bolton's treatment of subordinates and dismissive comments on the U.N.
Asked if the president had any reservations about Bolton's fitness for the post, White House press secretary Scott McClellan replied: "Absolutely not."
Bolton has addressed all questions about his record and behavior by testifying before the committee and offering additional answers to the panel in writing, McClellan said.
Several Republicans have made it clear they have reservations, that the president could have chosen someone better for the post, but it would be extraordinary for a Republican to vote against one of the Mr. Bush's nominees, reports CBS News Capitol Hill Correspondent Bob Fuss.
At least one Democratic senator, Sen. Christopher J. Dodd, D-Conn., said he would ask for a closed session so the committee could hear from intelligence officials about information Bolton requested relating to National Security Agency communications.
According to a spokesman for Dodd, Bolton asked for and received the identities of 10 U.S. officials involved in such secret NSA interceptions during the past four years.