The resolution, which passed late on Friday, said "the environmental disaster" resulted in an oil slick that covered the entire Lebanese coastline and extended to the Syrian coastline, causing extensive pollution.
Israel has been asked by the UN to compensate Lebanon before but this was the first time a price was put on the damages, AP reported.
General Assembly resolutions are not legally binding but they do reflect world opinion. The assembly voted 170-6 in favour, with three abstentions. Israel, the US, Canada, Australia, Micronesia and Marshall Islands voted "no".
The General Assembly acknowledged the conclusions in an August report by Ban Ki-moon, UN chief, that studies show the value of damage to Lebanon amounted to $856.4m in 2014. It asked Israel to provide "prompt and adequate compensation".
The General Assembly also asked Ban to urge UN bodies and other organisations involved in the initial assessment to conduct a further study, building on the work conducted by the World Bank, to measure and quantify the environmental damage sustained by neighbouring countries.
The resolution notes that "the secretary-general expressed grave concern at the lack of any acknowledgment on the part of the government of Israel of its responsibilities vis-a-vis reparations and compensation" to Lebanon and Syria for the oil spill.
It notes that Ban concluded that the spill is not covered by any international oil spill compensation funds and therefore recognises "that further consideration needs to be given to the option of security the relevant compensation from the government of Israel".
Nawaf Salam, Lebanon's UN ambassador, said his country considers the resolution to be "major progress" because it puts forward a figure for compensation, acknowledges the conclusions of Ban's report, and reaffirms the General Assembly's commitment to justice.