He will head up a new communications team working with Chelsea's chief executive Peter Kenyon. He will be responsible for overseeing Chelsea's communications with fans, the media and sponsors.
"Chelsea will continue to be one of the most exciting stories over the next few years and Simon will play a key role in communicating our aims and ambitions both on the field and off the field," said Kenyon.
Greenberg, 34, started his career on the Hornsey Journal in 1991 and has held senior editorial roles at both the Mail on Sunday and the News of the World.
He said: "I would not have left the Evening Standard or Associated Newspapers for any other paper or newspaper group. But to be a key part of the most exciting football project in years was an opportunity too good to pass up and I am looking forward to working with the great team of people who are already at Stamford Bridge, on and off the pitch."
Chelsea recently announced the appointment of Helen Wood, from UEFA, as chief press officer, who joins the club in June.
Chelsea Village the holding company for the business, built around Chelsea Football Club. It also includes a leisure and entertainment complex.
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