The Classic Gold network, featuring Tony Blackburn in the breakfast shift, currently has a 0.7% share of listening, as does Capital Gold.
GCap, which already owned 20% of the Classic Gold business and sold its airtime, has paid £3.95m in cash for the other 80%. This values the whole business at £4.94m and gives UBC a profit of £2.5m.
The licences were bought by UBC in 2000 and 2002 from GWR, which merged with Capital in 2005 to form GCap.
Ralph Bernard, chief executive of GCap, said: "Acquiring these stations will enable us to create a single classic hits network with the potential to become a fast-growing national brand as audiences increasingly migrate to digital platforms."
UBC's motive for the sale was the declining profitability of the stations and its need to focus on its production and DAB music download services.
Simon Cole, chief executive of UBC, said: "UBC is now concentrated on building service businesses rather than owning broadcast licences."
However, the company still owns 49% of digital station Oneword, of which Channel 4 is the controlling shareholder.
UBC today issued a trading update claiming its full year results will be in line with expectations citing strong advertising revenue performance in the last quarter.
But it has delayed the full commercial launch of its music download service, which allows people to buy tracks directly from radio stations, due to the lack of availability of devices capable of delivering the service.
Currently, the Lobster mobile phone, equipped with a DAB chip, is the only device and Heart in London is the only station offering the service. Since it launched in March 1,600 tracks have been sold.
UBC now believes that its service will also be attractive to owners of the emerging generation of in-home internet-connected digital radios.
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