The 33-year-old was charged with improper conduct by the FA after he had referred to Cole as a "choc ice", which was believed to be a racial reference.
Ferdinand denied the charge, claiming that the term is used to describe someone who is fake.
However, his protests have fallen on deaf ears and the FA have now issued him with a fine.
A statement on the FA's website read: "Manchester United's Rio Ferdinand has been fined £45,000 after an Independent Regulatory Commission found proven a charge of improper conduct in relation to a comment posted on Twitter.
"The Commission decided that the comment was improper and brought the game into disrepute. In addition, the Commission found that the breach included a reference to ethnic origin, colour or race.
"Ferdinand was fined £45,000 and warned as to his future conduct."
Ferdinand has not appealed the decision.