The Ohio House approved the measure 76-14 on Wednesday and Gov. John Kasich is expected to sign it.
The bill was championed by Republican Senate President Keith Faber after top state law enforcers raised legal concerns about the so-called Internet cafes.
The Senate also approved an effective statewide ban on such businesses on Wednesday.
Legislative efforts follow lawsuits and raids in Cuyahoga and Richland counties by Ohio Attorney General Mike DeWine, who says the operations harbor illegal gambling.
Defenders say the parlors are legal and shutting them down will cost thousands of Ohio jobs.
The state's current moratorium expires in June.