While working for RR Donnelley in the USA in the early 1990s, Simpson was hand-picked as production editor by then-Economist Group chief executive Marjorie Scardino. At the time, colour separations for the title's US edition were flown out by Concorde every week.
Scardino subsequently asked her to relocate and join the Economist's London-based production team in 1995.
Group director of operations Alan Dunachie lauded Simpson for doing "a fantastic job", and said: "Sharon has always been the ultimate production person. Absolutely in control, knows what's going on and runs a tight ship.
"During her time here, she and her department rose to the challenge of our global expansion: the circulation rising four-fold, the introduction of on-the-run colour, more print sites, a multitude of ad editions and the launch of our now bi-monthly lifestyle magazine, Intelligent Life. Week in, week out the Economist production department get it together and get it out, and that's very much about the skills and care Sharon has put into her job," he said.
Simpson, who now plans to return to the United States, was presented with a special farewell cover of The Economist featuring her face morphed onto the Statue of Liberty.
She said: "I've had a great career in print, considering I was originally planning to become a corporate attorney!
"I work with a fantastic team and they will do whatever it takes to get this publication out on time. The suppliers we have are the best of the best and I thank them."
Simpson will not be directly replaced. Production operations manager Simon Maggs and analysis and reports manager Faye Jeacocke will now report directly Dunachie.