Lakhdar Brahimi, 78, will succeed Kofi Annan, who resigned earlier this month after his six-point peace plan failed to achieve a meaningful ceasefire.
China was the first nation to give its reaction, promising to “co-operate positively” with Lakhdar Brahimi.
However, fighting has continued unabated in the northern city of Aleppo and the capital, Damascus.
Explosions were heard in a number parts of the Syrian capital overnight.
In Aleppo, government troops repulsed attacks by rebel forces near the airport on Friday, Syria’s state-run media said.
Rebel commanders also said they were fighting near the airport, telling the New York Times that their fighters had advanced to within metres of the airport fence.
The claims have not been verified independently.
Lakhdar Brahimi, whose appointment came a day after the UN called an end to its military observer mission, has held a long series of high-profile diplomatic posts.
As a senior Arab League official between 1984-91, Lakhdar Brahimi brokered an end to the Lebanese civil war, going on to serve as Algerian foreign minister between 1991-3.
Later, he was twice appointed as the UN’s top envoy for Afghanistan, from 1996-8 and from 2001-4. He has held similar roles for Haiti and South Africa.
A spokesman for Secretary-General Ban Ki-moon said the UN welcomed Lakhdar Brahimi’s willingness to help stop “the violence and suffering in Syria”.
Announcing his resignation earlier this month, Kofi Annan had said he was unable to fulfill his role because of the growing militarization of the conflict, as well as the deadlock over the issue in the UN Security Council.
Russia and China have vetoed resolutions on the crisis three times, citing their opposition to any action which might be seen as regime change imposed from outside.
Co-operation was essential in order to find a peaceful resolution, said Lakhdar Brahimi.
“There is no doubt that I will be able to do strictly nothing if I do not have the support and if I do not have the co-operation of the Syrians,” he said.
But Lakhdar Brahimi also insisted diplomatic efforts should not be abandoned: “These missions have to be undertaken. We have got to try. We have got to see that the Syrian people are not abandoned.
“I might very well fail but we sometimes are lucky and we can get a breakthrough.”
At least 60 bodies were found earlier this week in the Damascus suburb of Qatana, activists said, following what the opposition described as a “massacre” by government forces.
A poor-quality video posted online showed what appeared to be the charred remains of dozens of people, many with their hands tied behind their backs.
Activists estimate about 20,000 people have died since anti-government protests erupted against the Assad regime in March last year. Tens of thousands of people have also fled the country.
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