Brown Shipley is moving to 3 Hardman Street in Spinningfields, Manchester.
Allied London Properties sold 3 Hardman Street in Spinningfields last month to European fund manager Ærium.
The building was sold for £183.5m based on total rental income of £11.8m a year, reflecting a net initial yield of 6.1%.
Brown Shipley, which has had a close association with Manchester for nearly 150 years, is occupying around 14,500 sq ft at the building for an undisclosed sum. The firm also has offices in London, Edinburgh, Birmingham and Leeds. The move will involve all 80 staff at its King Street office moving into 3 Hardman Street.
Ian Sackfield, Brown Shipley's managing director who is based in Manchester, said: "As a modern private bank, with tremendous heritage, being part of the newly created financial district is very appropriate for Brown Shipley. This new office development is truly fantastic both in terms of style and all practicalities as we continue to expand our business and enhance our private client experience."
Mike Ingall, chief executive of Allied London, added: "We are delighted that Brown Shipley is moving to Spinningfields, they are an important organisation and fit directly with the type of customer that we developed 3 Hardman Street for. Brown Shipley is one of the most focused private banks in the city of Manchester and we want to see them prosper and grow.
Matthew Dobson, partner at solicitors Brabners Chaffe Street, completed the legal work for Brown Shipley's move which is planned for late September and will involve all 80 staff.
OBI Property's offices partner, Will Lewis, advised Brown Shipley on the search of its new premises to meet its requirements.
Brown Shipley will join other tenants including M&S, lawyer Pinsent Masons, Bank of New York Mellon, and accountant BDO Stoy Hayward at the 393,000 sq ft 3 Hardman Street, which was completed in 2009.
The sale to Ærium still allows Allied London to continue to manage the multi award-winning building.