A national newspaper's website picked up on the tweets - sent in 2012 - on the day Robinson was handed his England cap and took two New Zealand wickets as England struggled at Lord's.
The pace bowler was quick to issue a statement via the ECB which said: "On the biggest day of my career so far, I am embarrassed by the racist and sexist tweets that I posted over eight years ago, which have today become public. I want to make it clear that I'm not racist and I'm not sexist.
I deeply regret my actions, and I am ashamed of making such remarks. I was thoughtless and irresponsible, and regardless of my state of mind at the time, my actions were inexcusable. Since that period, I have matured as a person and fully regret the tweets.
"Today should be about my efforts on the field and the pride of making my Test debut for England, but my thoughtless behaviour in the past has tarnished this.
"Over the past few years, I have worked hard to turn my life around. I have considerably matured as an adult. The work and education I have gained personally from the PCA, my county Sussex and the England Cricket team have helped me to come to terms and gain a deep understanding of being a responsible professional cricketer.
"I would like to unreservedly apologise to anyone I have offended, my teammates and the game as a whole in what has been a day of action and awareness in combatting discrimination from our sport. I don’t want something that happened eight years ago to diminish the efforts of my teammates and the ECB as they continue to build meaningful action with their comprehensive initiatives and efforts, which I fully endorse and support.
"I will continue to educate myself, look for advice and work with the support network that is available to me to learn more about getting better in this area. I am sorry, and I have certainly learned my lesson today.
Tom Harrison of the ECB added: "I do not have the words to express how disappointed I am that an England Men’s player has chosen to write tweets of this nature, however long ago that might have been. Any person reading those words, particularly a woman or person of colour, would take away an image of cricket and cricketers that is completely unacceptable. We are better than this.
"We have a zero-tolerance stance to any form of discrimination and there are rules in place that handle conduct of this nature. We will initiate a full investigation as part of our disciplinary process.
Our England Men’s Team, alongside others from the ECB and our partners across the game, worked together today to create a moment of unity. Using today’s spotlight to reaffirm our commitment to driving forward an anti-discrimination agenda. Our commitment to that effort remains unwavering, and the emergence of these comments from Ollie’s past reiterates the need for ongoing education and engagement on this issue."
Robinson's county, Sussex Cricket, also issued a statement. It said: "There is simply no place for discrimination of any kind in cricket or anywhere else. We’re committed to making cricket in Sussex a game for everyone, so it goes without saying that we were beyond disappointed to read these tweets when they were brought to our attention today. Their content was wholly unacceptable.
"We are pleased that Ollie has apologised unreservedly and taken responsibility for a significant mistake that he made as a teenager. His age does not excuse the content of these tweets in any way and he will now suffer the consequences of his actions.
"In the years since the tweets were posted, Ollie has matured hugely. The Ollie Robinson we know at Sussex is very different from the young man that sent these tweets. We know he recognises the severity of the situation and that he is devastated that what should have been a proud day has been overshadowed in this manner. We know also that Ollie will learn some very important lessons from this experience. We will be here to offer any support Ollie needs during that process."