His appointment is in line with international growth plans by RBC, which advises agencies on business building and merger activity and which last year saw more than half its fees come from abroad.
The arrival of Jones ends RBC's two-year search for a non-executive chairman.
Graham Beckett, the company's founder, relinquishes the chairman's role but remains as chief executive. He said: "We're always advocating to our clients that they should appoint non-executive chairmen, so it's reasonable that we should take some of our own medicine."
Jones quit JWT in January 2001 at the age of 45 following serious health problems. He has since made a full recovery.
Jones, who started his career at Saatchi & Saatchi, spent 16 years at JWT, including a spell as its managing director. He is based in New York but is relocating to London and will spend about two days a month with RBC.
He said: "Results is the only firm specialising in advising on making transactions successful in this field, and on the creation and building of value that precedes it."