The 33-year-old marketing executive went missing just three miles from where Kate and her sister Pippa used to share a flat in Chelsea, southwest London.
The Duchess, 39, visited Clapham Common to lay flowers with other mourners in the days after Ms Everard’s body was found earlier this month.
She is thought to have also sent a message to Ms Everard’s family.
A source told The Mirror: ‘This was a deeply personal and heartfelt letter, simply to express her absolute sadness at what Sarah’s family and loved ones are going through.
The Duchess of Cambridge was seen placing daffodils at the vigil for Sarah Everard on Clapham Common earlier this month
‘The Duchess knows that no words can change what has happened, but wanted to let them know that they and Sarah are in her thoughts.
‘She remembers what it is like to walk alone as a young woman in London, and elsewhere, and like so many other women she has been thinking deeply about her experiences during those times.
‘It was important for her to pay her respects in this way.
‘This was a private matter to her and she wanted to show unity with everyone else who shares these feelings.’
A separate source close to Ms Everard’s family said they were ‘extremely touched’ to have received the letter.
Kensington Palace said it would not comment on private correspondence.
Durham University graduate Ms Everard went missing on March 3 while walking home after visiting a friend
The Duchess had made a private visit to the bandstand in Clapham Common where mourners placed flowers and cards earlier this month.
The mother-of-three laid daffodils and paused for a moment to reflect on the dozens of bouquets.
Later police were criticised for their heavy-handed treatment of women who attended a vigil at the site, which officers said was in breach of Covid rules.
Durham University graduate Ms Everard went missing on March 3 while walking home after visiting a friend.
Her body was found in woodland near Ashford in Kent a week later.
Serving Metropolitan Police officer Wayne Couzens, 48, from Deal, also in Kent, has been charged with her murder.
Couzens, a married father-of-two, worked in Scotland Yard’s Parliamentary and Diplomatic Protection Unit.
His plea hearing has been scheduled for July 9, while a provisional trial date has been pencilled in for October 25.