This is sadly not really true, especially in China, the biggest electric vehicle market, where most of the electricity is coal-generated. You end up with a car requiring more energy (e.g. more fossil fuels) to produce AND to run.
The situation is not very pretty in the USA yet either, but if you are hopeful in the next decade that the USA will decarbonate their electricity, then maybe you will get a positive return on GHG emissions over your car lifetime.
Electric cars as a means to reduce GHG emissions todaly only make real sense in specific countries with a low-emissions electricity profile, such as France and northern Europe (Sweden etc).