The Glasgow band, who been shortlisted four times for the honour, were recognised ahead of Biffy Clyro, Stanley Odd and The Snuts.
Mogwai were honoured for As The Love Continues, their tenth studio since forming more than 25 years ago. It was nominated for the Mercury Prize earlier this year.
Mogwai guitarist Stuart Braithwaite dedicated the award to the band’s long-time booking agent Mike Griffiths, who passed away earlier this month.
The award, which comes with a £20,000 prize, is one of the most lucrative in the UK cultural scene.
Ten years of the award, which has previously been won by Auntie Flo, Sacred Paws, Anna Meredith, Kathryn Joseph, RM Hubbert and Young Fathers, were celebrated in a lavish ceremony at the Usher Hall in Edinburgh.
Mogwai guitarist Stuart Braithwaite said: “I really was not expecting this. I have not thought of anything to say other than thank you and I wish I’d got steaming.
“This has been a really mental year for the band. Loads of things have happened that we didn’t think would happen and this is just another. This is nuts.
"I want to thank everyone who has bought the record, supported the record, played it on radio and all that stuff.”
The ten shortlisted albums in contention for this year’s SAY Award were whittled down from 327 eligible releases during the Covid pandemic between June 2020 and May this year.
Others contenders included AiiTee, Joesef, Lizzie Reid, Rachel Newton and The Ninth Wave.
The Usher Hall audience was treated to performances by Hamish Hawk, Sacred Paws, Bemz and Alasdair Roberts and last year’s winner, Edinburgh-based rap star Nova, who opened the ceremony, which was hosted by broadcasters Nicola Meighan and Vic Galloway.
Rising Edinburgh singing star Lvra, who was born in the city to Chinese parents, was honoured with a new Sound of Young Scotland Award and also took to the stage to perform, including a finale with Nova.
The 21-year-old released an EP last summer that she said sought “to paint a positive image of Chinese culture in the wake of Covid-19” at a time when racist attacks on Chinese students were on the rise.
Morag Macdonald, youth music initiative manager at Creative Scotland, said: “Using East-Asian, R&B and electronic music influences, Lvra’s music offers a refreshing and punchy alternative pop sound.”
The ceremony also saw Frightened Rabbit crowned the inaugural winner of a new award to recognise a ‘Modern Scottish Classic' album, with the group recognised for ‘The Midnight Organ Fight’.
The band was honoured three years after the death of singer Scott Hutchison, who took his own life.
Grant Hutchison, his brother and bandmate, said: “All of us can come at it from the same place that all of you can – this was and is Scott’s album.
"These are his words and they should be shared by all of us. It’s amazing to have an album that’s 13 years old and still inspires artists today, because it still inspires me everyday.”