The Guardian's successful bid of 195p a share is a 40% premium on the company's share price on May 3, its last day of trading before the newspaper group made its offer.
The bid will please Jazz FM's biggest shareholder Clear Channel, which originally wanted 220p a share for its 30.9% stake in the station, plus the 1.1% its executive director Roger Parry owned.
Just two weeks ago, Clear Channel and Parry accepted the Guardian's 180p-a-share bid after rival offers for the station failed to appear. This gave the Guardian, which already owned 18.5% in Jazz FM, backing from 51% of the station's shareholders.
At that time, the only hurdle in the group's way was Jazz FM's largest institutional investor, Herald Investment Management, with a 7.7% stake in the broadcaster, which had said it would hold out against the 180p-a-share bid. It is believed that the new bid appeased Herald.
The Guardian, one of Jazz FM's founding shareholders when the company launched in 1990, is expected to delist Jazz FM from the Stock Exchange.
The deal adds Jazz FM in London and its sister station in the North West of England, launched in 1994, to the Guardian's radio portfolio. Its radio interests include Real Radio in South Wales, Central Scotland and Yorkshire.
The company also acquires music labels Hed Kandi, Jazz FM and Stereo Sushi.
The move is the first sign of consolidation in the radio industry since the government removed barriers stopping radio groups from merging in its draft communications bill, which was unveiled last month.
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