The 27-year-old was fined 3,200 pounds ($4,400) and handed an eight-game ban, five of which are suspended for two years. He missed England's second Test against New Zealand and two T20 Blast games for his county during an investigation over the comments on Twitter.
The initial one-game suspension was imposed by the England and Wales Cricket Board (ECB), before Robinson withdrew himself from selection for his county side Sussex for the T20 games.
Robinson has admitted to breaching two ECB directives in relation to a number of offensive comments he made on Twitter in 2012-14 that came to light during his England debut in the drawn first Test against New Zealand in June.
"I fully accept the CDC's decision. As I have said previously, I'm incredibly embarrassed and ashamed about the tweets I posted many years ago and apologise unreservedly for their contents," Robinson said in a statement.
"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 offence. This has been the most difficult time in my professional career for both my family and myself.
"Whilst I want to move on, I do want to use my experience to help others in the future through working with the (Professional Cricketers’ Association)."