Brahimi is scheduled to assume his new position Sep 1.
The UN chief Friday met Brahimi, a former Algerian foreign minister, at the UN Headquarters in New York.
Brahimi was appointed last week to replace Kofi Annan, who would step down at the end of this month as the international mediator on the 18-month old Syrian crisis, Xinhua reported.
The UN chief said that Brahimi could count on the full backing of the international community when he assumes his position.
"You have all the respect and full support of the international community," Ban told the new special envoy. "It is crucially important that the Security Council and all the United Nations systems support your role."
Starting next month, Brahimi will be fully engaged in good offices on Syria on behalf of the UN and the Arab League. Earlier this week, the UN said that Brahimi would be based in New York.