The Spain international was suspended after a regulatory commission ruled he had stamped on the ankle of Liverpool's Emre Can in the 12th minute of Tuesday's League Cup semi-final second leg at Stamford Bridge, which Chelsea won 1-0 to complete a 2-1 aggregate victory.
There is no right of appeal and Costa will now miss the Premier League leaders Chelsea's match at home to title rivals Manchester City on Saturday and subsequent games against Aston Villa and Everton.
Chelsea manager Jose Mourinho insisted the incident, reviewed on video by referee Michael Oliver after he did not see it at the time, was "absolutely accidental".
Costa denied the charge of violent conduct levelled against him on Wednesday ahead of Thursday's 1800 GMT deadline.
However, the charge was upheld Friday and banned immediately.
"Diego Costa will serve a three-match suspension with immediate effect after a charge of violent conduct against him was found proven by an independent regulatory commission today (Friday)," said a statement issued by the Football Association, the English game's governing body.
"The Chelsea forward had denied the charge in relation to an on-field incident involving Liverpool's Emre Can which occurred in the 12th minute of the League Cup semi-final second leg at Stamford Bridge on Tuesday, January 27, 2015.
"The incident was not seen by the match officials but caught on video."
Source : AFP