The hospital, which has a population of 290 residents, made the announcement ahead of Friday’s VE Day commemorations.
Five of the deaths occurred in the hospital, while four veterans died while receiving hospital treatment, it said.
The hospital also confirmed that 58 residents have recovered after either testing positive or showing symptoms of COVID-19.
General Sir Adrian Bradshaw, governor of the Royal Hospital Chelsea, said: “Most of our Pensioners have risked their lives serving our nation through war and conflict somewhere in the world, just as our NHS staff and care workers are providing vital and sometimes dangerous service to the nation here at home during this Covid crisis.
“We salute all those working in the health and care sectors at this time and we understand only too well the difficulties that they face.”
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He said the hospital now has the capacity to test all those who show symptoms of the disease as well as all those living and working in the same accommodation areas.
General Bradshaw said the hospital would be marking VE Day “in a manner appropriate to the current situation”, saying residents would enjoy some “internal, socially-distant events” but they would be “against the backdrop of the recent losses we have suffered”.
He added: “We will reflect on the debt that we owe to those who served the nation in every capacity during the Second World War in Europe.
“Especially, as we are a home for veterans, we will remember those who were in our armed forces, several of whom are living here in the Royal Hospital.”
Following the announcement, Chelsea FC tweeted: “All of us at Chelsea Football Club send our deepest condolences to the family, friends and all those who are associated with the Chelsea Pensioners, following today’s sad news.”
All of us at Chelsea Football Club send our deepest condolences to the family, friends and all those who are associated with the Chelsea Pensioners, following today’s sad news. 💙— Chelsea FC - #StayHomeSaveLives (@ChelseaFC) May 7, 2020
One of the residents to lose their lives was 75-year-old Fred Boomer-Hawkins, who died on April 1.
Mr Hawkins had spent 20 years with the Royal Green Jackets infantry regiment and became a Chelsea Pensioner in 2017.
In a tribute on Facebook, his son Terry Hawkins said: “Sadly at 21:34hrs on 1st April 2020 my dad left us after becoming another victim to this deadly virus.”
Describing his father’s last moments, he wrote: “If the government showed footage of someone at the end with this virus it would scare people and they would heed the advice I am sure.
“Please all stay home, keep your distance, wear a mask and wash your hands. If not you might put someone you love through this.
“My dad was a great man, he was much loved by many and will be sorely missed.”