Staffline Group plc has agreed to buy the Sheffield company’s shares for £23.5m and will assume its net debt of £11m.
It is understood that Ms Harrison held 85 per cent of shares in A4e.
Staffline provides outsourcing, training and employability services.
Andy Hogath, chief executive of Staffline, said: “We are delighted to be announcing today the acquisition of A4e.
Kings Tower Sheffield: 40-storey 'student' block planned for High Street branded 'farcical'
Cole Brothers Sheffield: New future for former John Lewis department store is confirmed
Cole Brothers Sheffield: Sheffield MP Clive Betts slams listing as 'real obstacle' to developers
Cole Brothers Sheffield: Grade II listing of former John Lewis slammed as 'ludicrous decision'
New cafe 'Joni' opening up in Sheffield serving varied range of brunch, lunch and breakfast options
“This is an exciting milestone in Staffline’s growth, considerably expanding the size and geographic reach of our employability offering and will result in the combined business being one of the largest Work Programme providers in the UK.
“The significant strengths of both businesses will be united and we are confident that our leading position will be a strong platform from which to develop our strategy, services and innovation.
“We look forward to creating a winning team and business, and delivering significant shareholder value.”
Staffline said the acquisition represents a highly complementary fit with its existing employability
division and would accelerate the group’s growth strategy and bring a number of strategic benefits and revenue synergies.
Andrew Dutton, group CEO at A4e, said: “We are today starting a new chapter in the history of A4e.
“Staffline is exactly the right fit for us: its ambitions, robust financial position and its people and business values will all support the combined business as we grow together and build on our position as a leading Work Programme provider in the UK.
“A4e is now in the perfect ownership to both develop our customers and support our employer relationships and wish the combined business every success in the future.”
Ms Harrison, who founded the business in 1991, was advised by a team from Deloitte led by practice senior partner Martin Jenkins.
Mr Jenkins said: “We are delighted to announce the successful sale of A4e to Staffline.
“This acquisition makes great strategic sense for both companies creating a clear market leader and providing a base for further development.
“The management team at A4e have done an excellent job in developing A4e and building an attractive platform which will create more opportunities for its people under Staffline’s ownership.”
Ms Harrison, a former advisor to the coalition Government, stepped down as chairman in 2012 when allegations of fraud first emerged although there has never been any suggestion of wrongdoing on her part.
Last month, six employees were jailed following a £300,000 fraud in the Thames Valley area.
A4e has been subjected to thorough and extensive auditing by external bodies in the last few years.