Morgan has been at the telecoms firm since 2004. He oversaw the recent root and branch review of BT's comms spend and PR agencies.
He will now join Rolls-Royce as head of corporate affairs. The firm manufactures engines for civil aerospace, military vehicles, and is also active in the marine technology, nuclear and energy sectors. Previous comms chiefs include Colin Duncan, Chris Springham and Maria Derby Walker.
Morgan told PRWeek: 'I am leaving one great company for another. I have worked with a terrific team at BT and wish them every success in the future. But I believe in embracing change, and Rolls-Royce offers me a wonderful new challenge. This will be a global role, reporting to the CEO Sir John Rose and joining the Roll-Royce group executive. I will be responsible for the group's internal and external communications and for government relations around the world, so there should be plenty to fill my days.'
He joins Rolls-Royce in mid-November, and replaces Charles Blundell, who is moving to a part-time role and working on projects for the firm.
Morgan is a former BBC international business correspondent and has also worked at Weber Shandwick.