Jahangir Akhtar stepped down temporarily from his position at the authority, and as vice-chairman of the South Yorkshire Police and Crime Panel, in August.
It followed the publication in The Times newspaper of a woman’s account of being allowed contact with the alleged abuser from 1999, when she was aged 14.
In a statement, South Yorkshire Police said officers had investigated the allegations, and added: “South Yorkshire Police has now completed the inquiry and found no evidence to substantiate the claims.
“South Yorkshire Police do not intend to proceed further with this inquiry unless further evidence comes to light.”
Martin Kimber, Chief Executive of Rotherham council, said: “South Yorkshire Police have confirmed that the investigation has found no evidence to support the reported allegations, and will not be taking any further action.
“We would like to thank South Yorkshire Police for carrying out a thorough investigation and setting out their position in clear terms.”
Councillor Shabana Ahmed, press spokesman for Rotherham’s Labour group, confirmed Mr Akhtar had returned to both his previous positions.
She said: “The police have carried out a thorough investigation and we are all very pleased they have found no evidence in support of what was in The Times.”
Mr Akhtar’s accuser was one of four women who said they planned to sue Rotherham council for “systematic failures to protect them from sexual abuse by predatory men” when they were children.
Rotherham found itself a focus of concerns about under-age teenage girls being groomed for sex in 2010 when five men were given lengthy jail terms.