The announcement was made during the World Economic Forum in Davos, Switzerland.
As of January 2015, the UN has already received about $1 billion or two-thirds of the sum previously requested. However, the same amount needs to be transferred to the UN's World Health Organization (WHO), UNICEF and the World Food Programme to put an end to the epidemic, Nabarro said at a briefing.
"We have a very attractive and promising situation that leads us to believe that we're beginning to see the end of the outbreak," Nabarro said.
The current Ebola outbreak started in southern Guinea at the end of 2013 and later spread to Liberia, Sierra Leone, Nigeria, and Senegal, with several Ebola cases having been reported in the United States and Europe.
According to the latest WHO data, there have been about 8,500 reported Ebola-related deaths in Liberia, Sierra Leone and Guinea.