The band made the announcement on Tuesday through their official website.
The Rolling Stones have cancelled their Australia and New Zealand tour
"The Rolling Stones are deeply sorry and disappointed to announce the postponement of the rest of their 14 ON FIRE tour of Australia and New Zealand following the death of L'Wren Scott.
"Mick Jagger, Keith Richards, Charlie Watts and Ronnie Wood wish to thank all of their fans for their support at this difficult time and hope that they will fully understand the reason for this announcement."
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The statement also revealed the band plan to reschedule the postponed shows at a later date.
Mick Jagger and L'Wren Scott had been together for 13 years
Earlier on Tuesday, Mick Jagger wrote a heartbreaking post on his personal website in which he described his devastation at the death of his longtime girlfriend.
"I am still struggling to understand how my lover and best friend could end her life in this tragic way," the Rolling Stones band member wrote on his website in a post titled 'L'Wren'.
"We spent many wonderful years together and had made a great life for ourselves."
His tribute was written below a beautiful picture of the statuesque fashion designer, who had been his partner for nearly 13 years.
He continued, "She had great presence and her talent was much admired, not least by me.
L'Wren Scott was found dead on Monday morning
"I have been touched by the tributes that people have paid to her, and also the personal messages of support that I have received."
Concluding, he said, "I will never forget her."
The rock legend's note came just 24 hours after it was revealed that L'Wren had been found in her Manhattan apartment.