Willis Group Holdings P.L.C. has offered approximately €550 million ($594.4 million) to acquire the remaining 70% of French broker Gras Savoye & Cie. that it does not currently own, Willis said Wednesday.

Following the completion of the transaction, Gras Savoye will become part of Willis Group but will maintain its name and brand in key markets, including France.

Together, the two firms combined would have a presence in 131 countries, 84 of which would be wholly owned operations, the broker said in a statement.

Willis made its initial investment in Gras Savoye in 1997 and owned as much as 49% of the company. In 2009, Willis entered into an agreement with the company’s family shareholders and Astorg Partners in which each entity assumed nearly 32% ownership. In 2013, Willis extended a call option to buy all of Gras Savoye until June 2016.

The transaction is expected to close on or around Dec. 31, subject to customary regulatory consents and approvals, and acceptance of the firm offer by Gras Savoye’s shareholders.

Bringing the deal forward to 2015 “shows our enthusiasm” for the deal and “there was no advantage in waiting for a further six months,” said Dominic Casserley, CEO of Willis, in an interview.

Willis expects to see “significant revenue synergy opportunities” as a result of the deal, he said.

In particular, Gras Savoye will provide Willis with an established network of offices in Africa and several Eastern and Central European countries, in addition to extensive operations throughout France, Mr. Casserley said.

And the brokerage “plays in both the property/casualty and benefits space, which aligns very well with our strategy,” he said.

“In most markets where there’s a national health care system and the system comes under pressure, the supplemental benefits market around it is a burgeoning market,” he said, referring to France’s government-run health care system.

“The board of Gras Savoye is delighted to receive the offer from Willis Group. We have worked together for 40 years, and this offer is the logical next step in that relationship,” Patrick Lucas, chairman of Gras Savoye, said in the statement.

In addition to its offer, Willis has issued notice preserving its right under an existing shareholder agreement to acquire the remaining shares in Gras Savoye in June 2016, should this offer not be accepted.

In that event, the purchase price would be determined by a formula under that earlier agreement.

For the year ended Dec. 31, Gras Savoye’s net revenue was approximately €370 million ($447.7 million), with earnings before interest, taxes, depreciation and amortization of approximately €65 million ($78.6 million). Willis reported revenues of $3.8 billion in 2014. The combination of Willis, Gras Savoye and Miller Insurance Services L.L.P., which Willis is in the process of acquiring, will ensure that Willis’ revenues are “well, well north of $4 billion,” Mr. Casserley said.

Willis is the world's third-largest insurance broker, according to Business Insurance's latest ranking.