Sebastian, 29, the third oldest of Eubank’s five children, was a boxer like his father, fighting in light-heavyweight bouts.
He also made his MMA debut last year.
The father-of-one was found dead on a beach in the UAE where he lived with wife Salma and son Raheem.
He went by the name of the Alka Lion and fought in two professional fights, winning both.
Distraught Chris Eubank Snr, 54, said: “Never did I ever imagine I would write these words or experience the feeling I now have at the loss of my son.
“My family and I are devastated to hear of the death of Sebastian just days before what would have been his 30th birthday.
“He leaves his wife Salma, his son Raheem born just a month ago, his mother Karron Meadows, brothers Nathanael, Chris, Jr, Joseph, one sister Emily and countless relatives and friends.
“Sebastian grew up in Hove in England but in the last few years made his life in Dubai where he had a wide circle of friends and was a leader in the adoption of a healthy lifestyle and of alternative therapies.”
The boxing legend added: “As well as being a personal trainer and professional boxer, Sebastian was also a deep thinker who liked to challenge accepted wisdom.
“He was loved and respected by all who knew him and will be forever in the thoughts of friends and family. As a family we now kindly ask to be given space and privacy to celebrate his life and remember the son, the brother, the husband, the friend.”
Sebastian’s mother Karron Meadows said: “Our whole family is grieving at the huge loss of our son and brother, Sebastian. Please respect our grief and privacy while we try to comprehend our loss.”
His brother, Chris Eubank Junior, who is also a professional boxer, said on Twitter: “Rest easy little brother, I love you and you will be missed always.”