McDonald's also said last month that it would replace plastic straws with paper ones in the United Kingdom and Ireland from September.
Similar proposals are being considered elsewhere, including in NY and San Francisco.
McDonald's shareholders voted down a proposal requesting a report on plastic straws in May.
Starbucks said that it will begin using the strawless alternatives in Seattle and Vancouver stores by this fall, and expand to the US and Canada, followed by other global locations, in fiscal year 2019. Straws add up to only about 2,000 tons of the almost 9m tons of plastic waste that hits waters each year. Oakland and Berkeley, California, and other cities have also banned the use of disposable straws.
A global rollout of the strawless lid will begin in Europe, starting with select stores in France and the Netherlands.