Thompson will join the City agency next month as an associate partner.
It is thought that he will continue his focus on retail and leisure in his new job.
RLM Finsbury said his specific role and client duties were yet to be determined, but the agency does have a strong retail client list that includes Sainsbury’s, Alliance Boots, Marks & Spencer and Home Retail Group.
Thompson has worked at the Independent Group for over five years, most recently working across The Independent, i, Independent on Sunday and Evening Standard.
RLM Finsbury currently represents one fifth of the FTSE 100, according to Adviser Rankings.