Dawson is understood to be working with Michael Henson, a recently-departed London-based partner at financial PR firm Sard Verbinnen, to set up a new IR and corporate advisory business that will launch in 2018.
Dawson, who officially leaves Rolls-Royce in March, has been with the firm for more than two years. His previous employers include the National Grid, Cadbury and ICI.
Rolls-Royce's IR team will now be led by Jennifer Ramsey, formerly a fund manager at investment managers Sarasin & Partners. She leads a team of five at the 50,000-person global business.
Ramsey said: "I am delighted to have joined Rolls-Royce as head of investor relations. I bring with me almost twenty years of experience as a portfolio manager and an external perspective as an experienced capital markets participant and long-time user of investor relations."
Prior to joining Sarasin & Partners, Ramsey worked at TRW Investment Management as a pan-European active equity fund manager and before that was at JPMorgan in New York, where she was a private client portfolio manager.
Rolls-Royce also has a new corporate affairs director - Barney Wyld joined the company in October after three years at Network Rail.