The council selected Mr Ban as successor to Secretary-General Kofi Annan, whose 10 years in office expire on December 31.
His ascension comes amid the North Korean nuclear crisis.
The 192-member UN General Assembly must give final approval to Mr Ban's nomination, which usually follows within a week or two. That vote is expected to be positive.
Mr Ban, speaking to reporters in Seoul after the Security Council vote, said North Korea's nuclear test was "a grave and direct threat to peace and stability on the Korean peninsula and Northeast Asia."
"This should be a moment of joy but instead I stand here with a very heavy heart," he said.
Shortly after nominating Mr Ban, the 15 Security Council ambassadors went into closed consultations on North Korea to see what action could be taken after Pyongyang’s announcement of a successful nuclear weapon test.
The council on Friday had urged North Korea not to carry out a test, warning of unspecified consequences if it did.
"I think the fact the candidate is current foreign minister of the Republic of Korea is an asset in dealing with the situation in the Korean peninsula that we are now facing," Japan's UN Ambassador Kenzo Oshima told reporters.
Some diplomats, including Mr Oshima, have speculated that North
Korea's October 3 announcement of plans to carry out the underground nuclear test was timed, in part, to coincide with Mr Ban's candidacy in an effort to get world attention.
Mr Ban, 62, would be the eighth secretary-general in the world body's 60-year history.
He will inherit a bureaucracy of 9,000 staff, a US$5 billion (A$6.74 billion) budget and more than 90,000 peacekeepers in 18 operations around the globe that cost another $5 billion.
US Ambassador John Bolton immediately emphasised the need for UN management reform.
"With this vote today, the winds of change at the United Nations have started to rise and we are looking forward to some significant steps in the reform process when he takes office," he told news agency Reuters.
Mr Annan welcomed the nomination.
He said he had the "highest respect" for Mr Ban and would do "everything possible to ensure a smooth transition," a spokesman said.
The low-keyed Mr Ban will be a contrast to Mr Annan, a Ghanaian who in his first five years won a Nobel Peace Prize and was sometimes dubbed a diplomatic rock star, before financial scandals took over headlines in the past few years.
Mr Ban won't be "the sort of activist diplomat, ready to seize the initiative, which we saw in Kofi Annan," said Dick Leurdijk, a UN expert at the Netherlands Clingendael Institute of International Relations.
"I think he will be more like his Asian predecessor U Thant, who just took care of the shop," he said, referring to the Burmese diplomat who held the post from 1961-71.
US welcomes appointment
The United States urged rapid UN approval of Mr Ban Ki-Moon, expressing confidence the veteran diplomat will actively reform the world body.
State Department spokesman Sean McCormack said the US "welcomes" Monday's Security Council decision recommending Mr Ban to replace outgoing Secretary General Kofi Annan, who frequently found himself at odds with Washington during his 10 years in office.
"We look forward to prompt action by the UN General Assembly to appoint
Foreign Minister Ban so that he may begin to prepare for the challenges awaiting him and the United Nations," Mr McCormack said.
"The United States believes that Secretary General-designate Ban is the right choice to lead the United Nations at this pivotal time in its history," he said.
The administration of US President George W. Bush, notably through its outspoken ambassador-designate to the UN John Bolton, has been a leading critic of what it sees as inefficiency and mismanagement at the United Nations.