It is Four's seventh acquisition since acquiring £10m of equity finance from the Business Growth Fund in 2015, and its second this year after buying public affairs firm ICG.
Legend Engage's main services are data-driven social & digital insights, strategy and engagement, and clients include the BBC Good Food Show, Guinness World Records, HRA Pharma, Puressentiel and GSK.
Employing 12 people, with a network of 15 further consultants, the agency earned fees of £840,000 in 2016. It will move immediately to Four's HQ in London Bridge, becoming known as Four Engage.
The team will roll out its suite of proprietary data products, which all carry the Mapper360 brand, across Four's business, in particular its sector teams in health, travel, financial services, property and hospitality.
Legend Engage was founded in 2013 by Kath Ludlow and Rachel O'Sullivan, both of whom become managing directors of Four Engage.
Nan Williams, Four Communications Group chief executive, said: "When the opportunity arose for an acquisition grounded in real-time, tangible data and insights, we knew it would power our offering to the next level."
Since the BGF funding in August 2015, Four has acquired MSA Media, Broadgate Mainland and FBA in 2015, Packer Forbes and Rain Communications last year, and ICG in January. It had also made one acquisition a year in the four years prior to that, including Consolidated PR (2014) and Colman Getty (2012).
Legend Engage was advised by agency broker Mark Madsen on its sale - he said it was the fourth sale to Four on which he has advised.
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