Update, 8/6/13, 5 p.m. EDT: The ninth paragraph of this story has been revised to incorporate the names of additional Simpson Thacher & Bartlett lawyers who have roles in this transaction.

In a deal between two private equity firms that values the company changing hands at $4.4 billion, Apax Partners has agreed to sell global insurance brokerage Hub International Limited to funds advised by Hellman & Friedman. Kirkland & Ellis is advising Apax; Simpson Thacher & Bartlett is advising Hellman & Friedman.

The deal, which was announced Monday, is expected to close by the end of 2013, according to a Hub press release announcing the transaction. The Hub release said that while the Hellman & Friedman funds will have a majority stake in the brokerage, the company’s senior management is getting “a significant equity position.”

London-based Apax—whose other holdings include ALM Properties, the owner and publisher of The Am Law Daily— teamed with Morgan Stanley’s private equity arm to buy Chicago-based Hub for $1.7 billion in 2007 on the way to taking the company private.

Since then, Hub has grown to the point that it was ranked the tenth-largest insurance broker in the world based on its 2011 revenue by Business Insurance. In 2012 alone, Hub acquired 29 brokerages and launched the regional operations HUB Atlantic and HUB CFR in, respectively, the Maritimes and Oklahoma, according to a company press release.

HUB International CLC has also formed a new regional hub in the Caribbean, as well as buying San Juan, Puerto Rico–based insurance brokerage Carrion, Laffitte & Casellas. Once the various new additions are accounted for, Hub—which has 6,500 employees in the United States, Brazil, and Canada—estimates that its 2013 revenue will reach $1.2 billion.

Kirkland & Ellis is advising Apax in connection with the transaction. The firm’s team is being led by partners Srinivas Kaushik and Leo Greenberg, both of whom specialize in corporate, M&A, and private equity matters. The Kirkland associates working on the deal are Dylan Hanson, Meghan McKeever, David Rosenthal, and Joshua Soszynski.

Kirkland has represented Apax on numerous previous deals, including the private equity firm’s purchase of retailer Cole Haan from Nike $570 million in cash in November 2012; the acquisition by funds advised by Apax and JMI Equity of software vendor Paradigm for $1 billion in June 2012; and the combined acquisition of enterprise business software maker Epicor Software Corporation and business management software provider Activant Solutions for $2 billion in April 2011.

For its part, San Francisco–based Hellman & Friedman is relying on frequent outside counsel Simpson Thacher & Bartlett in connection with the deal.

The Simpson Thacher team on the matter includes M&A partners Andrew Smith and Richard Capelouto. Other Simpson Thacher partners working on the deal include Bill Brentani (capital markets), Tristan Brown (executive compensation and employee benefits), Katharine Moir (tax), Rise Norman and Daniel Webb (capital markets), Chad Skinner (equity coinvestment), Brian Steinhardt (credit), and Tom Wuchenich (funds). The team also includes senior counsel Steven DeLott (insurance). Associates from the firm who are working on the transaction are John Delfino, Michael Isby, Brian Korchin, Timothy Mulvihill, Zara Ohiorhenuan, Brian Price, Ravi Purushotham, Jodi Sackel, Leah Shen, Jason Vollbracht, and Jennifer Wolff.

Simpson Thacher has previously advised Hellman & Friedman in connection with its $1.8 billion bid to acquire the education unit of SunGard Data Systems in September 2011. The firm represented the private equity shop on its joint takeover, with the Carlyle Group, of contract drug researcher Pharmaceutical Product Development for $3.9 billion in October 2011.