The 34-year-old Portuguese only took over as manager in June 2011.
Former Chelsea midfielder Roberto di Matteo has been put in charge as first-team coach on an interim basis until the end of the season.
A statement on the club's website read: "Unfortunately the results and performances of the team have not been good enough and were showing no signs of improving at a key time in the season.
"The club is still competing in the latter stages of the UEFA Champions League and the FA Cup, as well as challenging for a top-four spot in the Premier League, and we aim to remain as competitive as possible on all fronts.
"With that in mind, we felt our only option was to make a change at this time."
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