The purchase price reflects a net initial yield of 5.7%.
Helical Bar said the acquisition of the 250,000 square foot building will be funded through a combination of cash and existing undrawn debt facilities.
Rents at the Grade II listed Churchgate House and Lee House, located on Oxford Street, currently go for between GBP14.00 and GBP17.50 per square feet.
The firm said a number of tenants extended their leases over the last 18 months. However, there is currently around 35% vacant, providing Helical with opportunities to improve income through letting up space.
The deal comes just weeks after Helical sold Battersea Studios in south London to Schroder UK Property Fund in a deal worth GBP35 million.
"Following the recently announced sale of Battersea Studios, we are very pleased to be able to quickly recycle the capital into a property where we see opportunity for good cash flow and capital growth," Investment Director Duncan Walker said in a statement.
"Churchgate and Lee House represents a high quality, well-located multi-let asset in a market that is starting to show the early signs of improving occupational demand underpinned by economic growth across the UK," he added.