Feltham, who spent over 30 years at the LSE before leaving in 1999, will join Holborn on 1 July.
Since leaving the LSE, Feltham has, as a financial consultant, advised auditing companies on setting up operations in tax havens and tax-efficient jurisdictions. From 2001 to the end of last year, Feltham worked as a consultant for US IT company Mantas, advising it on the development of anti-money-laundering software.
He has also been a director of AIM-listed financial services investor and pub-owner Caplay since 2004.
As the LSE's head of surveillance, Feltham was responsible for the scanning of all LSE transactions for irregular price movements that might indicate market manipulation, fraud or insider dealing.
The role involved liaising with City watchdog the Financial Services Authority and the FSA's US counterpart, the Securities and Exchange Commission.