Hayden died at the age of 35 after several days in intensive care at Cesena’s Maurizio Bufalini Hospital.
The American collided with a car last week while cycling in Italy.
The 2006 MotoGP champion was surrounded by his family in the final hours.
Hayden’s brother, Tommy said in a statement: “On behalf of the whole Hayden family and Nicky’s fiancée Jackie I would like to thank everyone for their messages of support – it has been a great comfort to us all knowing that Nicky has touched so many people’s lives in such a positive way.
“Although this is obviously a sad time, we would like everyone to remember Nicky at his happiest – riding a motorcycle. He dreamed as a kid of being a pro rider and not only achieved that but also managed to reach the pinnacle of his chosen sport in becoming World Champion. We are all so proud of that.
“Apart from these ‘public’ memories, we will also have many great and happy memories of Nicky at home in Kentucky, in the heart of the family. We will all miss him terribly.
“It is also important for us to thank all the hospital staff for their incredible support – they have been very kind. With the further support of the authorities in the coming days we hope to have Nicky home soon.”
The world of motorsport has united with numerous tributes paid to Hayden today.
British F1 driver Hamilton posted an image of Hayden on his Instagram with the caption: “Dear Nicky, you will be missed. May God hold you high, you are forever in our hearts.
“My thoughts and prayers to you and your loved ones.”
Former F1 champion Jenson Button tweeted: “Totally shocked… Another one of the good guys gone way too soon. My thoughts are with his family and loved ones at this terrible time.”
Felipe Massa wrote: “R.I.P NickyHayden. My thoughts are with his family.”
Sir Chris Hoy said: “Just awful…RIP Nicky Hayden.”
And British MotoGP ace Cal Crutchlow wrote a lengthly message saying: “Every motorcycle racer and fan around the world should and probably does look up to this guy. I did, and still do. The best professional I have ever had the pleasure to meet, share a track with and be a friend of. RIP @nicky_hayden. Our thoughts are with Jackie and the whole Hayden family.”
