The Argentine was shown the red card after conceding a penalty for shouldering Sunderland's Steven Fletcher off the ball as he attempted to reach a through pass.
"An independent regulatory commission found the match referee had made an obvious error in dismissing the Newcastle United defender for denying an obvious goalscoring opportunity," the FA said in a statement on Tuesday.
Newcastle, however, have been charged by the FA for failing to control their players in the wake of the incident and have until Oct. 30 to respond to the charge.
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Steve McClaren's side, who were drawing 0-0 when Coloccini was sent off, are second from bottom in the Premier League with six points from 10 games.
(Reporting by Toby Davis; editing by Tony Jimenez)
