Kelley and Payne are scheduled for July 1 before U.S. District Judge Kate O'Malley.
Gallagher and Schuman are to appear before her on July 2.
All four were charged in what is known as an "information," where the defendants have been cooperating with authorities.
On July 28, in what has become known as the "Cuyahoga County corruption probe," about 175 FBI and IRS agents raided the offices, homes and businesses of several Cuyahoga County officials.
Since then, subpoenas have been served on nearly 100 others in relation to the probe. The four charged Friday were the first charged in the probe.
Kelley, Payne and Gallagher were charged with multiple counts of conspiracy, bribery, theft and filing false tax returns. Schuman was charged with conspiracy.
Payne and Gallagher are former chiefs of staff at the Cuyahoga County Engineer's office.
Kelley is a former county employee who worked at the engineer's office and in Cuyahoga County Auditor Frank Russo's office.
Schuman is the former director of Alternatives Agency Inc., a Cleveland halfway house.