The agency, whose clients include the Liberal Democrats, Young's Brewery and GlaxoSmithKline, will remain a standalone operation for the time being but will eventually be merged with Equanim, the Media Square marketing services subsidiary.
No job losses are expected among the 15 staff at the £6 million-billing shop. Bean is expected to take a senior role in the merged operation.
The deal is the culmination of several weeks of talks and follows the introduction of the two parties by a mergers and acquisitions specialist.
In recent years, Banc has been doing increasing amounts of consultancy work and is understood to have opted to sell because of difficulties in finding the financial resource to offer a fully integrated service.
Media Square, which was founded three years ago, has been carrying out an expansion programme since Kevin Steeds, the former Incepta finance director, joined as the chairman. It has offices in Leeds, Manchester and Oxford. Its recent purchases have included the FI Group, a direct marketing and online branding and design business, and Fourninety, an e-solutions company.
Steeds said Banc would not only give Media Square a foothold in the London market, but bring in a quality team of communications directors.
Bean, a former WCRS senior executive and one-time head of advertising for BT's consumer arm, set up Banc in 1996 with Mark Cramphorn, who quit last month.