Sgt Sean Preston died at the age of 50 on Friday (February 12), according to the Sussex Police Federation.
The Federation said he had been a police officer since 1996 and had been working at home for several months before being admitted to hospital early in the year after contracting Covid-19.
He leaves behind his partner, children and grandchildren.
The Federation added: "Sussex Police Federation would like to offer our condolences - and our thoughts are with Sean’s family, friends, and colleagues at this difficult time."
Donna Lonsdale, Deputy Chair of Sussex Police Federation, said: “We are all devastated by the news of Sean’s passing. I had the pleasure of working with Sean in Brighton and know he will be missed by all of his colleagues.
“Sean, who was a Custody Sergeant at Worthing, had been working from home for several months and was admitted to hospital early in the New Year for treatment after contracting the Covid-19 virus. Sadly he lost his fight yesterday (12 February).
“Sean really was a lovely guy - and when both Sussex Police Federation Chairman Daren Egan and I think of him, we do nothing but laugh. I can honestly say working with him was a pleasure and he is a huge loss to the police family.”