Private-equity firm Carlyle Group LP is buying a majority stake in Sedgwick, an insurance firm, in a deal the companies value at $6.7 billion.

Fellow private-equity fund KKR & Co., which currently is the majority owner of Sedgwick, will close out its stake when the deal is done, according to a joint release from Carlyle and Sedgwick on Wednesday. KKR bought its majority stake in Sedgwick in February 2014 for $2.4 billion.

The...