The Algerian was shown a red card by referee Mike Dean in the 15th minute for a challenge on defender Phil Jones in a 2-0 Premier League defeat to Manchester United on Monday.
West Ham manager Slaven Bilic decried the decision as harsh at the time, saying Jones had committed the foul and the club would appeal.
"West Ham United can confirm that a Football Association Regulatory Commission has upheld the Club’s claim for wrongful dismissal," West Ham said in a statement.
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"The Algerian is therefore eligible to play against Manchester City in the Emirates FA Cup third round on Friday evening and in the following Premier League fixtures with Crystal Palace and Middlesbrough."
Manchester City midfielder Fernandinho will have to serve a four match ban with immediate effect after his claim of wrongful dismissal was rejected.
The Brazilian international was sent off for a reckless two-footed tackle on Icelandic midfielder Johann Berg Gudmundsson in the 2-1 win against Burnley on Monday.
The usual three match ban was increased because it was his second dismissal in the league this season.
(Reporting by Alan Baldwin, editing by Brian Homewood)
