Global Radio says it is to buy GCap Media, the owner of Classic FM and Xfm, in a £375m deal.
Global, which owns the Heart and Galaxy radio stations, has been in talks with GCap since the beginning of the year and will pay 225p per share.
GCap, Britain's largest commercial radio group, had rejected two earlier offers at 190p and 202p.
Global said GCap was "a very strong business" and the deal would create a bigger rival for the BBC.
"We are delighted that the board of GCap has unanimously agreed to recommend our acquisition of GCap," said Charles Allen, Global's chairman and former ITV boss.
"We are excited by the opportunity to build on GCap's position as the leading commercial radio player and are committed to providing the best platform for both our advertisers and listeners."
The price tag is 18% higher than Global's initial 190p-a-share proposal put forward in December.
Global Radio, a privately held firm, is backed by horse racing tycoons JP McManus and John Magnier.
It was set up as a vehicle to buy radio stations and bought Chrysalis Group's stations last year for about £170m.
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