It was previously owned by Land Securities Group after it bought the site for £50m in May 2012.
Barney Rowe, partner at Orchard Street, said: "The Cornerhouse is a strong leisure asset with an impressive line-up of tenants, located in a city centre that is underpinned by strong demographic trends, including urbanisation and a flourishing university population.
"We are very pleased to increase our exposure to this ever more popular subsector where we are confident we can extract value over the long-term."
Polly Troughton, head of portfolio, leisure at Land Securities, added: "The sale of The Cornerhouse capitalises on the increased rental value we have created following our asset management strategy."
London-based Orchard Street Investment Management is a commercial property investment manager focused on the UK market, which acts on behalf of institutional clients worldwide to advise on investing in property. It has assets under management worth £5 billion.
St James's Place, headquartered in Cirencester, is a wealth management and financial planning firm.
It recently announced it will move its Nottingham office from Castle Boulevard to Embankment House.
Orchard Street was advised by Savills and JLL advised Land Securities.