Under the new rules, households will be fined $1 (Â£0.61) if their rubbish bins contain more than 10% food waste, and businesses and apartment buildings $50.
The city already recycles 56% of its waste but is aiming for 60% by 2015.
Seattle, in Washington State, is the second US city after San Francisco to make composting mandatory in an effort to reduce greenhouse gas emissions.
Composting is the processing of breaking down food and lawn refuse into useable soil through decomposition.
Up to 40% of food in the US is wasted, according to a report by the Natural Resources Defense Council.
Only 5% of food scraps are composted, according to the US Environmental Protection Agency (EPA).
Many Seattle homes and businesses have food compost bins but are not required to use them - now they will have to.
The city will begin issuing warning tickets on 1 January 2015 and fining customers on 1 July, according to the ordinance, which passed unanimously on Monday.
Under the new rules when Seattle garbage pickers see too much food waste in a rubbish bin, they will note it in a computerised system and the fine will be added to the customer's rubbish carting bill, local media reported.
Multi-unit flats and businesses will also be required to limit their food waste but will get two warnings before they are fined, according to the Seattle Times newspaper.
Seattle officials do not expect the programme to be a money-maker for the city, Tim Croll, the Seattle Public Utilities solid waste director, told the newspaper.
He added the city has collected less than $2,000 (Â£1,220) over nine years of a similar programme that banned recyclable items from the rubbish.
"The point isn't to raise revenue," Mr Croll said. "We care more about reminding people to separate their materials."
Correction 10 October 2014: This report has been amended to clarify that fines will apply for disposing of food waste incorrectly rather than doing so at all.

Images posted on social media showed flames emerging from many of the building's 24 floors.
There were no immediate reports of fatalities from the blaze, the cause of which is unknown.
A number of people were treated for smoke inhalation at the scene, officials told the Gulf News newspaper.
Residents were evacuated from the building and the power was cut, Brigadier Abdullah Al Suwaidi, head of civil defence in Sharjah, told Gulf News.
Around 200 families live in the tower, the newspaper said.
Images suggested that the fire started on one of the building's lower floors before spreading rapidly upwards. Flaming debris could be seen falling into the adjacent car park.
The blaze reportedly brought traffic to a near standstill in the roads around the building.
The Seattle city council has voted to fine businesses and residents that do not recycle their food waste.
[NEXT_CONCEPT]
A high-rise residential building in Sharjah in the United Arab Emirates has caught fire, sending plumes of thick black smoke into the air.