The appeal is on top of the $3.4 billion that the UN estimates is needed this year for the 13.5 million people still in Syria who have been affected by the conflict.
"Syrian refugees and host communities need our support now more than ever," UN High Commissioner for Refugees Filippo Grandi told an international aid conference in Helsinki.
"The international community must send a clear message that it stands with them and provides the urgently-needed support."
The appeal, by the UN and 240 partner agencies, is for what is called the Regional Refugee and Resilience Plan (3RP) for 2017 and 2018.
The $4.63 billion figure is the amount set for 2017. A funding figure has yet to be set for 2018.
The programme aims at financing and organising aid for 4.7 million refugees in Turkey, Lebanon, Jordan, Iraq and Egypt.
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These countries, which have borne the brunt of the refugee crisis sparked by the Syrian conflict, are struggling to meet the challenges triggered by the influx.
Grandi recalled that only 59 percent of the $4.54 billion target set for 2016 was actually met, leaving a $1.8 billion shortfall.
"Last year we reached funding percentages of close to 60 percent. I think that we can all do better," he said.
In addition to Syrians who have fled abroad, some 13.5 million people within the country are in desperate need of humanitarian assistance.
They include 6.3 million who have been internally displaced and 4.6 million who are in besieged and hard-to-reach areas.
"Civilians continue to be targeted in brutal attacks," Stephen O'Brien, emergency relief coordinator for the UN Office for the Coordination of Humanitarian Affairs, told the conference.
"The suffering of the Syrian people -– the majority of whom remain inside the country -– continues unabated. It's imperative that we step up our collective efforts," he said.