"We're absolutely made up that album has gone to number one," they said.
"From the scaffolding yard to the top of the charts, who'd have thought it? Up Stockport!"
The five-piece sold 9,500 more albums than their nearest rival, grime star Giggs, to secure the number one slot despite never having had a hit single - an indication of the increasing split between the singles and albums charts.
Last week's number one album, a posthumous release by Blossoms' former support act Viola Beach, drops to number five.
Top five albums
All Over The World - The Very Best Of
5) Viola Beach
Top five singles
1) Major Lazer feat Justin Bieber and MØ
2) DJ Snake feat Justin Bieber
Let Me Love You
3) Calum Scott
Dancing On My Own
4) Jonas Blue feat JP Cooper
5) Chainsmokers feat Daya
Don't Let Me Down
There are new entries for indie rockers Wild Beasts, whose fourth album Boy King debuts at nine; and emo band Moose Blood, who make their first appearance in the Top 40 with Blush, at number 10.
Elvis Presley's final studio recordings, compiled under the title Way Down in The Jungle Room, enter the chart at 16; while Dinosaur Jr's first album in four years, Give a Glimpse of What Yer Not, is new at 23.
It's not such good news for US producer DJ Khaled, whose latest album, Major Key, tumbles 27 places after debuting at number seven last week.
The singles chart is largely static, with most of the Top 10 shuffling down a place to accommodate Justin Bieber's new entry at two.
However, there are two major exceptions: Twenty One Pilots jump from 20 to nine with the glitchy ballad Heathens, taken from the Suicide Squad soundtrack.
And Chainsmokers' collaboration with US pop sensation Halsey, Closer, leaps from 33 to 12 - giving Halsey her first top 20 single in the UK.