Her body was found in her New York apartment on Monday. Investigators have ruled she committed suicide by hanging.
The Stones have cancelled their planned tour of Australia and New Zealand, reporting their priority is to support their singer through his ordeal.
Jagger says: “I am still struggling to understand how my lover and best friend could end her life in this tragic way.
“We spent many wonderful years together and had made a great life for ourselves. She had great presence and her talent was much admired, not least by me.”
“I have been touched by the tributes that people have paid to her, and also the personal messages of support that I have received. I will never forget her.”
Bandmate Keith Richards says: “Mick has always been my soul brother and we love him. We’re thick as thieves and we’re all feeling for the man.”
Ronnie Wood adds: “Right now the important thing is that we’re all pulling together to offer Mick our support. Without doubt we intend to be back out on that stage as soon as we can.”
Fashion designer Scott, who was 49, left no suicide note.