The £50 million deal sees the company acquire the stakes previously held by founder Alistair O’Reilly and a number of other shareholders.
Essex-headquartered Access provides software and services with a focus on financial management systems and human capital management.
It has clients including Topps Tiles, the National Museum of Science and Industry, Sue Ryder Care and Birmingham International Airport.
Bayne comments: ‘It’s fitting that on the 20th anniversary of Access’ incorporation we’ve agreed a deal which marks a significant step change in the speed and scale of the business expansion.’
Speaking on the future for Access, Bayne revealed that growth would be achieved through in-house development and acquisitions of complementary services.
Under the terms of the deal Jeremy Hand and Philip Buscombe, from private equity firm Lyceum Capital, will join the board of Access. O’Reilly and non-executive chairman Paul Druckman have left the company.