The celebrated US fashion designer was found dead in her New York flat on Monday, in an apparent suicide.
In a statement on his website, Sir Mick said he still failed "to understand how my lover and best friend could end her life in this tragic way".
He added: "We spent many wonderful years together and had made a great life for ourselves."
Sir Mick described his partner as having "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."
The Rolling Stones have now have cancelled the first date of their Australian tour following the news.
The British band, fronted by Sir Mick were due to play in Perth on Wednesday. Their promoter said no further information was available.
They are scheduled to play five more concerts in Australia. The following date from Perth is due to take place on 22 March in Adelaide.
The BBC's Phil Mercer said ticket holders for Wednesday's gig were being asked to hold on to their tickets until a further update is available.
Scott, who was believed to be 49, was found by her assistant at 10:00 local time (14:00 GMT) on Monday.
The Stones are due to perform in Sydney, Melbourne and Macedon later this month before playing two dates in Brisbane and Auckland, New Zealand, in April.
The On Fire tour is then scheduled to move to Europe in June, with concerts planned for the Netherlands, Germany, Italy and Belgium.
Sir Mick, 70, began dating Scott in 2001.
On Monday night, a spokesman for the singer issued a statement to deny a report that he had recently ended his relationship with the designer.
"The story in the New York Post re: a split between Mick Jagger and L'Wren Scott is 100% untrue," said his spokeswoman, Victoria Scarfone.
"There is absolutely no basis in fact to this story. It is a horrible and inaccurate piece of gossip during this very tragic time for Mick."
The UK's Press Complaints Commission (PCC) told the BBC it had received a small number of complaints from the public over images published which apparently showed an upset Sir Mick at the time he was told Scott had died.
It is understood the singer has not yet complained personally, but the PCC would deal with the matter in due course.
Supermodel Naomi Campbell, Vogue editor Anna Wintour and singer Madonna were among those who were fans of the designer.
Scott was found dead by her assistant 90 minutes after sending her a text message asking to come to her Manhattan apartment without specifying why, the Associated Press news agency reported.
Police said there was no sign of foul play and no note was found.
Naomi Campbell said Scott was "the epitome of elegance and femininity".
Anna Wintour described Scott as "a total perfectionist... always unbelievably generous, gracious, kind and so much fun."
She added: "Her old world American manners and charm were from another time, but her sensibility was always fiercely modern."
Madonna wrote in a statement: "This is a horrible and tragic loss. I'm so upset. I loved L'Wren's work and she was always so generous with me."
Actress Nicole Kidman, said to be a friend of many years, was "heartbroken and in shock right now and unable to say anything", according to a spokeswoman.
Bianca Jagger, one of Sir Mick's former wives, tweeted: "Heartbroken to learn of the loss of the lovely and talented L'Wren Scott. My thoughts and prayers are with her family. May she rest in peace."
According to its last UK filing Scott's firm, LS Fashion Limited, owed creditors about $7.6m (Â£4.6m), as of 31 December 2012. It had assets of $1.7m.
Scott's death comes a month after she cancelled a show at London Fashion Week, saying production delays had left key pieces unready for the show.
Scott, born Luann Bambrough, was raised by Mormon adoptive parents in the US state of Utah.
The 6ft 3in (1.9m) tall former model began her career in Paris, then moved to Los Angeles to become a fashion stylist, according to a biography on her company's website.
She founded her own high-end fashion label in 2006 and created a more affordable line of clothes with Banana Republic.
Scott had dressed actresses such as Oprah Winfrey, Sarah Jessica Parker and Angelina Jolie for red carpet events.
She was also a costume consultant for films such as Ocean's Thirteen and Eyes Wide Shut.
Sir Mick Jagger has said he is "struggling" to understand the death of his girlfriend L'Wren Scott.