Marsh and Jelf have agreed the terms of a cash takeover of the broker in a deal valuing Jelf at £258m.
Talks about the possible deal were first confirmed on 19 August.
Marsh will pay 215p per share funded from existing cash resources and the wider group.
The price represents a 4% uplift on the closing price of Jelf's shares on 18 August.
The deal will see Jelf, which was founded in 1989, bringing 37 offices across the UK to the Marsh brand.
It also adds 100,000 business and individual
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