The four-piece, from Whitburn denied US pop star Demi Lovato the crown after a closely-fought race this week.
Fronted by 26-year-old singer and guitarist Jack Cochrane, The Snuts also become the first Scottish band in 14 years to enter at number one with their debut, since The View's Hats Off To The Buskers in 2007.
Titled W.L., the album pays tribute to the Whitburn Loopy, the trouble-makers and youths from their hometown, and had been backed in the race for number one by fellow chart-topping Scot Lewis Capaldi.
In a video appeal across social media, Capaldi urged people to download and buy the Whitburn band’s new album.
In his video, Capaldi said: “We all love Demi Lovato but sometime we have to make sacrifices.”
The band, who became friends at school, also top this week's vinyl albums chart and the record store chart.
"This one is for all the fans who have proved that it's possible to get a band like us to number one," they said.
"Every copy you bought of this record goes a long way. It's old school and it's beautiful. Thanks very much - we love you."
The Scottish Music Industry Association said: "A huge congratulations to The Snuts for landing a UK number one album with WL. As the first Scottish band to do so with their debut record since The View's Hats Off to the Buskers in 2007, this is an incredible achievement; not least at a time of significant challenges industry wide.
"Their success follows on from Mogwai claiming the number one spot just a few weeks back with As The Love Continues, highlighting the strength, passion and determination from Scotland's artists and music industry, and signifying an exciting and impactful period of engagement and connection with Scottish music."
Former child star Lovato settled for the runner-up slot but still claimed her highest-charting record in the UK to date with Dancing With The Devil... The Art of Starting Over, which details her recovery from addiction and abuse.
On the singles chart, Lil Nas X lands a second week at number one with Montero (Call Me By Your Name).