The deal will create the UK's biggest radio company, controlling 40% of the radio advertising market.
The merged group will own one national station in Classic FM, and 55 analogue stations and 93 digital stations, reaching approximately 18m listeners.
The name for the new company, GCap Media, was also approved.
GWR shares will be delisted and new Capital Radio shares issued to GWR shareholders at 8am on May 9.
Capital is to sell off Nottingham-based 106 Century FM as a condition of the merger.
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