The two companies will now focus on formally putting the deal to the votes of both sets of shareholders, while the rest of the industry will be considering whether or not to bid for the Nottingham-based station.
The OFT made the station's disposal conditional to the deal in order to prevent the merged Capital/GWR from gaining a near monopoly on airtime in the region.
Capital said it would not make a formal announcement about the bidding process for Century until it was ready to reveal the winner.
John Myers, chief executive of GMG Radio, has said it will bid for the station, while Chrysalis, which already has Heart FM in the West Midlands, is also likely to be in contact with Capital.
The station has a weekly reach of 302,000 listeners in an area covering 2m potential adult listeners. It also broadcasts on DAB.
The other stations in Capital's Century network, including Newcastle, Manchester and Portsmouth, will be retained by the merged Capital/GWR.
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