Nelson, who joined the City shop in 2000 from stockbroker Albert E Sharp, where he was an investment manager, resigned from College Hill last week.
Nelson's boss Geoff Smith confirmed that he had quit the firm, adding that a replacement was being sought.
Nelson, who previously worked as an investment manager, is to join financial PR and IR shop Hansard Communications.
At College Hill, Nelson was one of three PROs working for its life science clients, which include Synergy Healthcare, the UK's largest healthcare sterilisation outsourcing firm.
Other PROs, such as partner Adrian Duffield, also worked with the life science division to service College Hill clients.
Hansard was founded in 2003 by former stockbroker Adam Reynolds.