It is understood FD has forked out around £4m for the consultancy, whose 30 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, who refused to comment on the terms of the deal.
He added LLM's 23 London-based staff would move into FD's offices in September and that the deal has been under discussion for sixth months. LLM, founded in New Labour's heyday in 1997, has annual fee income of just over £3m.
The purchase looks likely to spell the end of the LLM name from 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 FD Tamesis.
FD launched its first public affairs offering in March last year with an office in New York, currently staffed by 10 consultants.
The financial communications shop brought 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 Aon and risk consultancy firm Kroll.
According to LLM managing director Craig Leviton, seven of the consultancy's staff will gain equity in FD including directors and co-founders Ben Lucas and John Mendelsohn. Leviton will continue to lead LLM, reporting to Watson.
Neil Lawson, the firm's other founder, quit last year to work full-time at left-wing pressure group Compass. He became embroiled in the cash-for-ministerial-access allegations in 1998, which became known as lobbygate.
Lawson Lucas Mendelson was formed in June 1997 as a break away from Lowe Bell Political.
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