The term 'Jose Mourinho' is trending around the world in the US, Australia, India and parts of Africa.
Since news broke of the sacking there have been over 200,000 tweets.
A club statement said: "The club wishes to make clear Jose leaves us on good terms and will always remain a much-loved, respected and significant figure at Chelsea.
"His legacy at Stamford Bridge and in England has long been guaranteed and he will always be warmly welcomed back to the club.
"The club's focus is now on ensuring our talented squad reaches its potential.
"There will be no further comment until a new appointment is made."