The ordinances will come back to the council next month for a formal "second reading" and final approval.
The laws will take effect on Jan. 1 but won't be enforced until July 1.
Garth Schultz, the city's manager of operations and environmental services, said city officials will use that six-month period to educate local businesses about the new ordinances.
He said the grace period will also allow businesses to get new supplies and change their operations.
A summary of the plastic bag ordinance on the city's website states it's intended to reduce the use of single-use carry out bags and encourage the use of recyclable bags by consumers and retailers.
Among other things, it prohibits the free distribution of plastic bags to hold customers' purchases at stores in El Cerrito.
It would allow paper bags if the bags are made of at least 40 percent recycled content and customers are charged at least 5 cents for each bag.
A summary of the food container ordinance states its purpose is to eliminate the use of expanded polystyrene foam food containers and to encourage the use of compostable, recyclable or reusable food ware.
There have been concerns expressed about the impact on small businesses. However, Schultz said there has been no evidence of serious impacts in other cities that have already adopted similar ordinances.
He noted local business owners did not express concerns during the public hearings on the ordinances.