The bid values the UK's biggest radio firm at £370m, around 20% higher than Global's original offer in December of £313m.
GCap has now put out a holding response to the offer, which came in this morning, saying it will make a statement in due course.
The stock market reacted by driving the radio group's share price up 13.3% to 212.75p before falling back to 205.5p, up 9.5%, having closed at 187.75p last night.
Global stressed its willingness to secure approval for the deal from the competition authorities and promised GCap shareholders "cash and certain value today compared with the inherent execution risk" in GCap's new strategy.
The offer comes a day ahead of the deadline imposed on Global by the Takeover Panel to bid or walk away for six months, but one of the conditions is that GCap acts to extend the deadline to April 2.
This would allow Global to finalise its own financing arrangements and carry out due diligence on GCap's books.
Talks between Global's advisers and GCap's shareholders, which include the Daily Mail and General Trust, Fidelity and Schroders, took place last night.
GCap's board rejected the first offer without telling its shareholders and rejected the second, pitched at 202p, after consulting major shareholders.
Global's third offer statement says it believes that the "Final Proposal" offers substantially greater value than could be achieved by GCap on a standalone basis.
"Even if the planned cost savings and initiatives outlined in GCap's strategy announcement of 11 February 2008 can be achieved in full.
"In Global Radio's view, GCap faces considerable challenges given the current conditions in the radio, advertising and stock markets. The Final Proposal offers cash and certain value today compared with the inherent execution risk in GCap's strategy."
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