The merged company will be third largest by market capitalisation after Sedgwick and Willis Corroon.
JIB was floated in 1991 by Jardine Matheson, which still owns a 60 per cent stake. This will be diluted to 34 per cent after the merger.
Jardine is backing the deal, which was first discussed between the two brokers two years ago but put on ice because of uncertainties over the future of the Lloyd's insurance market which have now been resolved. Talks were revived about six weeks ago.
Ken Carter, chief executive of Lloyd Thompson, who will play the same role in the merged group, said the merger was not a defensive move just to make cost savings but intended to exploit the exact fit between the two.
His own firm was predominantly a London market insurance and reinsurance broker and had tried in recent years to develop in Asia and Latin America. JIB was "fantastically well established" in Asia Pacific because of its connection with Jardine.
The only area where there was a potential for conflict was in the London energy insurance market, but even there the two companies had different geographical specialities - JIB in Africa and Asia and Lloyd Thompson in America and Scandinavia, he said.
The new company, to be called Jardine Lloyd Thompson, will be chaired by John Barton, now chief executive of JIB, whose shares shot up 21p to 130p after the terms were announced. Lloyd Thompson rose 1.5p to 174p.
The offer, to be made by Lloyd Thompson through Phoenix Securities, is of four new Lloyd Thompson shares for every five JIB shares.