Guardian Media, which owns The Guardian and Observer newspapers, is offering 180p a share, a 29% premium on Friday's 139.5p closing price.
Paul Myners, chairman of Guardian Media, said the bid will give Jazz FM the economies of scale it needs to compete effectively in the UK radio industry.
Guardian Media already owns 18.5% of Jazz FM and said it had struck an agreement with US media group Clear Channel International, which owns 30.9% of the station.
"This, together with Guardian Media's excellent track record of managing radio stations, will benefit the business and its employees. The offer gives Jazz FM shareholders full and fair value, liquidity and certainty. We have made contact with the board of Jazz FM and are seeking their recommendation of the offer," Myners said.
The 12-year-old radio station broadcasts jazz, blues and soul music in London and the North-West. In 2001, it made a pre-tax profit of £134,000.
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