The office building had been owned by the Royal London Mutual Insurance Society but was put on the market for £40m in October.
The Grade I listed property has the two famous Liver Birds on its roof.
Along with the Cunard and Port of Liverpool Buildings, it is one of the Three Graces on the city's waterfront.
The 330,000 sq ft (31,000 sq m) building is currently home to companies including ITV and HSBC.
Thomas Landschreiber, chief investment officer of Corestate, said the company is looking to "invest significant funds to maintain and strengthen this city-building office building in the long term".
"As a new owner of this emblematic building, we appreciate its heritage and its importance to the people of Liverpool," he added.
Source: Museum of Liverpool
Liverpool's iconic Royal Liver Building has been sold for £48m to Luxembourg-based real estate investment manager Corestate Capital Holding.