Financial terms were not disclosed but Brand Learning Group has 120 staff with offices in London, New York and Singapore.
Mhairi McEwan, the chief executive and co-founder of Brand Learning Group, is described as the majority shareholder and Niall Fitzgerald, the former chief executive of Unilever and chairman of Thomson Reuters, is chairman and one of the other shareholders, according to Companies House filings.
Brand Learning will become part of Accenture’s Customer & Channels practice, rather than Accenture Interactive, the digital agency arm that has bought a string of creative and design agencies, including Karmarama and Fjord in the UK.
However, Accenture said Brand Learning "will also link with the digital design and engagement capabilities of Accenture Interactive".
Laura Gurski, senior managing director and head of Accenture’s Customer & Channels practice for consumer goods and services, retail, travel, life sciences, automotive and industrial industries, said: "Accenture’s acquisition of Brand Learning, with its impressive track record in building client capabilities in marketing and sales strategy and organisation change will further enable us to help clients deliver more integrated customer experiences across the organisation – to drive and manage that business growth."
She added that helping CMOs underpinned the rationale for the deal.
"More than 90% of CMOs say marketing will undergo fundamental change in the next five years, driven by analytics, digital and mobile technologies," Gurski said.
"With increasing digital innovation and personalised customer engagement, the marketing and sales functions are now seen as the key driver of top-line growth.
McEwan said the sale made sense because Accenture "is a leading global force in digital transformation" and her company will be able to offer clients "deeper consulting capabilities".
The most recent UK accounts for Brand Learning Group at Companies House show it made a pre-tax profit of £2.8m on turnover of £18m in the year to March 2016.
Typically, an agency is valued at up to two times annual revenues.
McEwan is one half of a power couple as her husband is Phil Bentley, the former British Gas boss, who went on to head Cable & Wireless Communications.
Corporate advisory firm Clarity advised Brand Learning Group on the sale.
Clarity previously worked on the sale of creative agency The Monkeys in Australia to Accenture in May,