Rybak, who was the business manager and financial secretary for the Journeymen Plumbers Union Local 55, pleaded guilty to the five counts against him: bribery-related conspiracy, theft from labor unions, theft from employee benefit funds and tampering with a witness, and conspiracy to tamper with a witness.
Rybak faces two years in prison.
According to the plea agreement, Rybak admitted doing favors for Dimora in exchange for Dimora using his influence to get county jobs for two union members and a raise for Rybak's wife, Linda.
Linda Rybak, an administrative assistant in the county's human resources department, had her office raided on July 28, 2008, when nearly 200 FBI and IRS agents conducted simultaneous raids all over Northeast Ohio.
Linda Rybak has not been charged with any crime.
He has also agreed to cooperate with authorities and testify against Dimora and other defendants in the ongoing corruption probe.
Rybak and Dimora were both indicted Sept. 15, along with Cuyahoga County Common Pleas Judges Bridget McCafferty and Steven Terry, Michael Gabor, and Jerry Skuhrovec
U.S. District Judge Kate O'Malley has set their trials to begin in September.