The 73-year-old Apprentice star paid tribute to Derek as he shared a picture of his sibling with fans.
He wrote: “My brother Derek died today another victim of Covid which complicated his underlying health problems.
“He was a life long Spurs fan and my sister in law made me laugh in 1991 thanking me for buying Spurs for him.
“He will be sadly missed by the whole family.
Lord Sugar has been outspoken during the Covid-19 pandemic – even falling out with his close friend Piers Morgan.
The pair had a bitter disagreement over the Government’s Coronavirus response and Lord Sugar has vowed never to speak to Good Morning Britain host Piers again.
Lord Sugar’s fury is based on a belief that Piers’ regular ITV breakfast show attacks on the Government during the Coronavirus pandemic were self-serving.
“He’s gone mad. Absolutely gone mad.”
Lord Sugar came under fire for spreading “fake news” on his Twitter account saying Coronavirus was man made and started in China.
The entrepreneur shared the “dangerous and irresponsible” view from a Japanese professor named Dr Tasuku Honjo who argued Covid-19 was created by humans in a laboratory.