Grousbeck is making the investment through Causeway Media Partners, a fund he set up in May and which has been backed by a number of NFL and NBA team owners.
Financial details were not disclosed but media reports said they were injecting $21 million into the project.
"We believe Formula E is a great evolutionary step in motorsport and a way to entertain millions around the world while driving the development of the best possible electric vehicles," Grousbeck said in a statement.
Formula E will stage its first race in Beijing next September and is planning a series of city centre races using battery-powered vehicles capable of speeds of 220 kph.
Spaniards Enrique Banuelos and Alejandro Agag have committed about $100 million to develop the format. Grousbeck will join the board of Formula E as part of the agreement.
(Writing by Keith Weir, editing by Pritha Sarkar)
