"The Secretary-General appreciates Mr Brahimi's willingness to bring his considerable talents and experience to this crucial task for which he will need, and rightly expects, the strong, clear and unified support of the international community, including the Security Council," said UN spokesman Eduardo del Buey.
The announcement confirmed what diplomats told Reuters on Thursday.
Brahimi, who hesitated for days to accept a job that France’s UN envoy Gerard Araud called an "impossible mission,” will have a new title, Joint Special Representative for Syria. Diplomats said the change was to distance himself from Annan.
UN Secretary-General Ban Ki-moon and Arab League chief Nabil Elaraby back his appointment, Del Buey said. Diplomats said all Security Council members support Brahimi.
UN officials told Reuters that Brahimi was expected to arrive in New York next week to meet with Ban and discuss plans for a fresh approach to the Syria conflict, which the United Nations says has killed over 18,000 people.
Del Buey said Ban thanked Annan, a Nobel Peace Prize laureate who accepted the job of Joint Special Envoy for Syria six months ago, "for his selfless efforts and contributions to the march for peace in Syria."
Annan, who is stepping down at the end of this month, has said his Syria peace plan was hampered by a divided UN Security Council.
Frustrated by deadlock
Annan was especially frustrated by the deadlock between the five permanent council members. Russia, backed by China, repeatedly vetoed Western- and Arab-backed resolutions that criticized the Syrian government and threatened it with sanctions, saying the United States, Europe and Gulf Arabs were seeking regime change.
The Western powers have accused Russia, Syria's top arms supplier and staunch ally, of propping up Syrian President Bashar al-Assad's government. They have also accused Syria’s ally Iran of providing military aid to Assad.
In an interview with France 24 television, Brahimi said he would soon meet with the Security Council.
"We are going to discuss very seriously how they can help,” he said. "They are asking me to do this job. If they don’t support me, there is no job. They are divided, but surely they can unite on something like this and I hope they will."
"Kofi Annan is a friend and I have been in touch with him throughout his mediation," Brahimi said. "I don't know whether I will succeed or whether I will fail like he did."
The UN mission of France, this month's Security Council president, reiterated on its Twitter feed the council's support for UN-Arab League mediation in Syria.
But council diplomats said privately that it will be extremely difficult for Brahimi to transform that expression of support into a binding sanctions resolution that would pressure the government and rebels to stop fighting. Annan had urged the council to adopt such a resolution, but Russia was opposed.
White House spokesman Josh Earnest described Brahimi as "a capable and seasoned diplomat," though he said the United States wants to know more about the UN plans for him.
"We need to hear more from the UN on the mandate of Mr Brahimi's new position," he said. "Our position and our view about the solution to this problem hasn't changed - that it’s time for President Assad to step down and to allow this political transition to move forward."
Diplomats said Brahimi wanted to adjust his mandate, but it was not clear how his approach will differ from Annan's.
The United States, envoys say, saw little point in replacing Annan and has stepped up non-lethal support to the rebels.
Brahimi, 78, has served as a UN special envoy in Iraq after the US invasion that toppled Saddam Hussein, in Afghanistan, both before and after the end of Taliban rule, and in South Africa as it emerged from the apartheid era.
The announcement about Brahimi was made as UN observers in Syria prepare to withdraw due to the violence.
Separately, Russia canceled a meeting on Friday of the permanent council members and key Middle Eastern nations on Syria, the so-called Syria "Action Group," after most participants failed to confirm attendance, UN diplomats said.
"Almost no one confirmed attendance, not the Americans, Europeans, Arabs," one diplomat told Reuters on condition of anonymity. "There wasn't much interest in this meeting."
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