According to the Official Charts Company (OCC), the band’s self-titled debut went straight in at the top of the charts after receiving support from BBC Radio 1, 2 and 6 Music.
The record, which was produced by The Coral’s James Skelly and Rich Turvey, sold more than 9,500 copies ahead of its nearest rival to finish at number one.
Speaking to OfficialCharts.com, Blossoms said: ‘We're absolutely made up that the album has gone to number one. From the scaffolding yard to the top of the charts, who'd have thought it? Viva Stockport!’
This week's runner-up is British rapper and grime artist Giggs.
His fourth studio album Landlord is 19 places higher than his previous best, 2013's When Will It Stop which reached number 21.
Elsewhere, indie rockers Wild Beasts scooped a second top 10 album with Boy King.