On Sept. 15, both McCafferty and Terry were indicted on federal charges. They technically remain on the bench but are disqualified from hearing cases, Brown said.
Both retired judges' appointments run through the end of the year.
Coyne is already hearing McCafferty's cases and Kelly will start hearing Terry's cases on Monday.
Taxpayers will be paying the salaries of both McCafferty and Terry, as well as the retired judges, according to state law.
McCafferty, a Democrat, is up for re-election and says she will continue to campaign and expects to be back on the bench next year. Michael Astrab, the Republican candidate for her seat on the bench, has asked her to resign.
McCafferty is accused of lying to federal officials in 2008 and is alleged to have had conversations with Cuyahoga County Commissioner Jimmy Dimora. Dimora was indicted earlier this month on 26 charges.
Terry is accused of conspiracy with ex-Cuyahoga County Auditor Frank Russo regarding a lawsuit that was before Terry.
McCafferty, Dimora and Terry have all pleaded not guilty and have maintained their innocence. Russo pleaded guilty to his charges and was sentenced to 21 years in prison.