Brough will take up the role later this month, after the departure of LSE Group's head of corporate comms John Wallis in July. A spokeswoman was unable to comment on Wallis' next move.
Brough has been head of external affairs, EMEA, for Thomson Reuters since 2008. Before this she spent a year as global head of financial PR for Reuters and held senior roles at Powerscourt and Citigate Dewe Rogerson.
In her new role, Brough will report directly to group CEO Xavier Rolet. In 2009, the London Stock Exchange appointed Citigate Dewe Rogerson as its corporate and financial public relations agency, replacing previous incumbent Finsbury.