UN chief Ban Ki-moon told participants at the meeting in Kuwait that four out of five people in Syria were living in "poverty, misery and deprivation".
"The Syrian people are victims of the worst humanitarian crisis of our time," he said.
Addressing the closing session of the Third International Pledging Conference for Syria, Ban welcomed the promised funds as "very generous".
The amount almost equals the combined total of USD 3.9 billion promised at the two previous conferences.
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The United States pledged $507 million and non-governmental organisations committed more than USD 500 million.
Other major contributions came from Britain with USD 150 million, United Arab Emirates with USD 100 million and Norway which promised USD 93 million.
Jordan and Lebanon, which together host close to 2.5 million refugees, were represented by their premiers who appealed for international aid to help their economies cope with the tragedy.
Qatar's Foreign Minister Khalid Al-Attiyah proposed to set up a special fund for the education of Syrian children.
The money pledged by the bloc consists of 500 million euros in "humanitarian aid, early recovery and longer-term stabilisation assistance" from the European Commission, with the balance coming in pledges from the bloc's 28 countries, the EU said.
"Four out of five Syrians live in poverty, misery and deprivation. The country has lost nearly four decades of human development," Ban said.
Kuwait has hosted a donor conference for Syrians in each of the past two years, generating several billion dollars worth of pledges.