It is understood FD has paid a mixture of cash and shares for the consultancy, whose 40 clients include KPMG, Merrill Lynch and Orange.
'We are well established in financial communications and issues management advice but public affairs has hitherto been missing,' said FD group chief executive Charles Watson.
He added that LLM's 23 London-based staff would move into FD's offices in September and that the deal had been under discussion for six months.
LLM, whose MD is Craig Leviton, was founded in New Labour's heyday in 1997 and has annual fee income of just over £3m. The purchase may eventually spell the end of the LLM name in the lobbying arena, although Watson said this was not on the immediate agenda.
At the start of the year, FD acquired property PR specialist Tamesis Communications, which is now in the process of being rebranded as FD Tamesis.
FD launched its first public affairs offering in March last year with an office in New York.
The financial comms shop bought itself out of Cordiant Communications two years ago, backed by private equity firm Advent International. FD and LLM have operated an informal alliance for five years, sharing clients such as insurance firm Aon and risk consultancy firm Kroll.
Leviton said he, with founding directors Ben Lucas and John Mendelsohn and the firm's partners, will gain equity in FD. Leviton will continue to head LLM, reporting to Watson.
LLM's other founder, Neal Lawson, quit last year to pursue a number of other interests including work for pressure group Compass.
Lawson Lucas Mendelsohn was formed in 1997 out of Lowe Bell Political.