The move will see managing director Joanne Varey become majority shareholder while Stephen Bentley, who acquired Granby from the Omnicom Corporation, will become chairman and remain a minority shareholder.
Craig Parsons, IT director at Granby, will also become a minority shareholder in the business.
The company is based in Blackburn, emplying over 100 people, and a spokesperson told Packaging News there was no restructuring planned.
It provides services such as direct marketing, e-commerce fulfilment, and warehousing and distribution to a blue chip client base which includes Sainsbury's, England and Wales Cricket Board, Department for Education and The Information Commissioner's Office.
"It's a fantastic opportunity for us to continue building on the growth and success Granby has undergone in recent years, " said Joanne Varey, managing director at Granby Marketing Services.
"Most importantly, it enables us to ensure we're still delivering a seamless experience and offering to our existing client base, whilst also giving us the tools and capabilities to seek new revenue prospects."
Enterprise Ventures provided $1.35m from its EV Growth fund to support the buy-out, with NatWest providing $600,000 term debt alongside a $500,000 working capital facility from RBS Invoice Finance, and the remainder coming from investment by directors.
Wayne Thomas, investment director with Enterprise Ventures, added: "Granby is a profitable, well positioned services business with an impressive, long-standing client base. It has invested heavily in IT over recent years to keep pace with new technologies. With large companies increasingly outsourcing non-core activities such as direct mail and fulfilment, the market is growing and Granby is well placed to take advantage of the opportunities."