Fulton spent almost three years in the role at McDonald's. Before this she held several senior comms roles in the food industry including at Nestle and Kellogg's. She also worked at Ketchum as an associate director for seven years.
Her new title at Unilever is director of comms for the supply chain, partnering the executive team led by Pier Luigi Sigismondi.
McDonald's confirmed the news but declined to provide further comment. It is understood that a replacement for Fulton will be announced in the coming days.
Fulton's departure follows news that McDonald's chief executive Don Thompson is stepping down after two-and-a-half years in the job, after the company reported a decline in sales last week.
Fourth quarter earnings were $1.1bn (about £0.7bn), down 21 per cent from the year before. Sales in the US market were down 4.1 per cent, as the fast food chain faces increasing competition from restaurants such as Chipotle and Shake Shack.
Thompson is being replaced by McDonald's current chief brand officer Steve Easterbrook, who will take up the role in March. Easterbrook, who is from the UK, previously ran the Pizza Express and Wagamama restaurant chains.