Robinson added: "I am deeply sorry for the hurt I caused to anyone who read those tweets and in particular to those people to whom the messages caused offense. This has been the most difficult time in my professional career for both my family and myself."
Robinson was also fined 3,200 pounds.
The CDC panel considered "the nature and content of the tweets, the breadth of their discrimination, their widespread dissemination in the media and the magnitude of the audience to whom they became available," it said.
Mitigating factors, it added, included the time that had elapsed since the postings and "a number of personal references which demonstrated that Robinson, who chose to address the panel, is a very different person to the one who sent the tweets."
Robinson had addressed the panel at a June 30 hearing.
"It also took account of his remorse, admissions and cooperation as well as the huge impact which the revelation of these tweets and its consequences have had upon him and his family," the statement continued.
Robinson has agreed to participate in anti-discrimination and social media training programs.
ECB chief executive Tom Harrison said Robinson "will now be available for selection for England again."
"Ollie has acknowledged that, whilst published a long time ago when he was a young man, these historic tweets were unacceptable," Harrison said. "He has engaged fully in the disciplinary process, admitted the charges, has received his sanction from the CDC and will participate in training and use his experiences to help others."
After Robinson's suspension last month, the ECB said it would review players' social media to "address any historical issues" and opened the door to taking disciplinary action against other players, if necessary.