Bone joins FH in mid-August, when financial services head Andrew Marshall will move to a senior director role, concentrating on client work after five years of co-heading the financial practice.
Bone's role will be managerial, and will give him responsibility for clients. He will report to chairman Neil Hedges.
During his nine years at Finsbury, Bone has led accounts including Standard Chartered, International Power and Bradford & Bingley, reporting to the agency's founder and chairman Roland Rudd. Before Finsbury he was an accountant at Price Waterhouse, rising to assistant manager in its European financial services practice.
Last month FH's financial practice recruited Hudson Sandler consultant James Benjamin. Clients include Bank of America and PricewaterhouseCoopers.
Meanwhile, Finsbury has recruited Sunday Telegraph companies editor Ed Simpkins to be one of eight associate partners.
Simpkins has been at the paper for six years, before which he was at commercial property trade magazine Estates Gazette.