In a message posted online, the Rolling Stones frontman said he will "never forget" the designer and former model who was found dead in her New York apartment yesterday morning.
The band, who were in Perth for a gig, cancelled their entire tour of Australia and New Zealand as a mark of respect.
Sir Mick said: "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. "
Scott, 49, had been dating the 70-year-old rock star since 2001 after they met when she was the stylist at a photoshoot.
Shortly after her death was announced yesterday, it emerged that her British fashion company had been losing millions of pounds.
Accounts filed with Companies House in October show that Scott's British company, LS Fashion Ltd, was running at a loss of more than £3.5 million in 2012, up from more than £2.5m the previous year.
The documents also show the firm owed more than a million pounds, despite having assets totalling a similar amount.
Scott, who was said to be 6ft 4ins tall and towered at least half a foot over her boyfriend, became well-known in Britain after she got together with Sir Mick.
She designed stage outfits for notable headline performances by the band at Glastonbury Festival and Hyde Park in recent years.
It is understood that police do not suspect foul play. Reports say she hanged herself.
A spokesman for Scott asked for the privacy of her family and friends to be respected.
Originally called Luann Bambrough, and brought up as a Mormon in Utah, she changed her name to launch her modelling career in her teens.
She worked in Paris for a number of years, with the likes of Thierry Mugler and Karl Lagerfeld, then returned to the US as a stylist. She was a wardrobe consultant for films such as Eyes Wide Shut and Ocean's Thirteen.
Scott launched her fashion line in 2006, with fans of her work said to include Sarah Jessica Parker, Nicole Kidman and Michelle Obama, and she has also designed for Banana Republic.