Video report by ITV News Correspondent Chloe Keedy
In a statement, the family said: "We can confirm that our Caroline passed away today, the 15th of February.
"We would ask that the press respect the privacy of the family at this difficult time and we would ask they make no attempt to contact us and/or photograph us."
A lawyer for the Flack family confirmed that Caroline took her own life and was found dead in her east London flat on Saturday.
Following Ms Flack's death, an ITV spokeswoman said: "Everybody at Love Island and ITV is shocked and saddened by this desperately sad news. Caroline was a much loved member of the Love Island team and our sincere thoughts and condolences are with her family and friends."
She entered a not guilty plea to the assault charge at Highbury Corner Magistrates' Court and she was released on bail with conditions that stopped her having any contact with Burton ahead of a trial due to start on March 4.
Ms Flack's management team criticised the CPS for pressing ahead with her "show trial" even though her boyfriend said he did not support it.
In a statement, Francis Ridley of Money Talent Management, said: "We are devastated at the loss of our client and friend Caroline Flack.
"An immensely talented young woman who was at the top of her game professionally and loved by television viewers across the country.
"In recent months Caroline had been under huge pressure because of an ongoing case and potential trial which has been well reported.
"The Crown Prosecution Service pursued this when they knew not only how very vulnerable Caroline was but also that the alleged victim did not support the prosecution and had disputed the CPS version of events.
"The CPS should look at themselves today and how they pursued a show trial that was not only without merit but not in the public interest. And ultimately resulted in significant distress to Caroline.
"Our thoughts are with Caroline's family at this time."
Tributes have poured in for the former Love Island presenter, including from Piers Morgan, Eamonn Holmes and new Love Island presenter Laura Whitmore.
Laura Whitmore, who took over Flack as host of Love Island ahead of the current season, tweeted: "I'm trying to find the words but I can't" with a broken love heart emoji and a picture of the pair together.
This Morning presenter Phillip Schofield paid tribute to Flack with a post on his Instagram stories.
He added text above a message that Flack had posted on social media, which read: "In a world where you can be anything, be kind".
Schofield wrote: "You poor darling girl my heart is breaking #BeKind".
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