Among the other benefits available to electric car owners are parking permits.
Amsterdam is the latest in a series of European cities to restrict polluting vehicles with the aim of improving air quality and reducing carbon emissions.
Last month, London began charging steep fees in the city center on cars that can't meet tough emissions standards. Paris plans to ban diesel vehicles by 2024, followed by gasoline cars in 2030.
Hamburg became the first German city to ban older diesel cars from some streets in May 2018, after the country's top court ruled such bans are legal. Other German cities followed with similar restrictions.
Countries are also taking action. The United Kingdom wants to ban sales of new gasoline and diesel cars starting in 2040. China, India, France and Norway have similar plans.
Amsterdam has already banned all diesel commercial vehicles and camper vans built before 2000, diesel taxis built before 2009 as well as buses that are more than 14 years old.
Diesel cars built before 2005 will be pulled off the city's roads starting next year.
Amsterdam struggles with air pollution despite being the cycling capital of Europe. Overall air pollution has decreased over the past decade but some busy streets still exceed EU standards.
The average resident will have their life cut short by more than a year because of dirty air, according to the city. Globally, 3.6 million people die each year due to pollution caused by fossil fuels, according to a recent study.