Ride-hailing companies Uber Technologies Inc. and Lyft Inc. are planning to give some drivers money to buy stock in their initial public offerings, a rare move that would grant them access to two of the most hotly anticipated IPOs ever.

Both Uber and Lyft’s IPOs will include programs that would give some of their most-active or longest-serving drivers a cash award with an option to put it toward stock in the IPOs, according to people familiar with the matter. It is typically hard for an ordinary investor to buy a company’s...