The FA's Independent Regulatory Commission imposed the penalty after Ferdinand responded to a message suggesting Cole was the "choc ice" in the trial of John Terry, who was accused of racially abusing Rio's brother Anton.
The term 'choc ice' is used to refer to a person who is 'fake', supposedly 'black on the outside but white on the inside'.
Ferdinand requested a personal hearing earlier in the month after being formally charged by the FA over the message.
But the commission has today announced that the comment "was improper and brought the game into disrepute".
It also noted the breach included "a reference to ethnic origin, colour or race".
Ferdinand was fined £45,000 and warned about his "future conduct". Both the FA and Manchester United were informed of the reasons behind the fine on Wednesday (August 15) and had until yesterday at noon to appeal.
On July 14, Ferdinand tweeted: "@carltonebanks I hear you fella. Choc ice is a classic! hahahahahha"
This was in response to the message: "@rioferdy5 looks like Ashley Cole's going to be their choc ice. Then again he's always been a sell out. Shame on him."
The previous day, former England captain John Terry had been cleared of racially abusing QPR footballer Anton Ferdinand. Cole was called as a defence witness in the trial.
Ferdinand's tweet was later deleted following a negative reaction from other users.
The Football Association said that it was not alleging Ferdinand was a racist, but rather his endorsement of @carltonebanks' tweet in a public forum was a "form of abuse" which had "brought the game into disrepute".
Ferdinand, who has 3m Twitter followers, had accepted that the term 'choc ice' was insulting and could only be used to refer to someone who was black or mixed race.
After finding him guilty, the FA's independent commission said that in calculating its fine, it took into account that Ferdinand had been the "poster boy" and role model to other professional footballers who were using Twitter, along with his background in anti-racism campaigns.
It also noted that the tweet was in response to another person's message, rather than an original tweet. This led the body to reduce the initially intended fine down by 25% to £45,000.