Federal authorities plan to unseal charges against a former top aide to New York Gov. Andrew Cuomo as early as Thursday in connection with an alleged bribery and kickback scheme involving the governor’s signature economic-development program, according to people familiar with the matter.

In addition to the former aide, Joseph Percoco, the U.S. attorney’s office in Manhattan intends to bring public-corruption charges against a number of other individuals in connection with the wide-ranging investigation, these people said....