Everything You've Come to Expect marks the band's second number one debut, after 2008's The Age of the Understatement also shot to the top of the countdown.
It also takes frontman Turner's tally of chart-topping albums to seven, as each of his releases with his other group, the Arctic Monkeys, also shot to first place in their native U.K.
Danish pop stars Lukas Graham are new at two with their self-titled debut, while the Pet Shop Boys enter at three with Super. Adele's 25 and Black Stone Cherry's Kentucky round out the new top five.
Meanwhile, in the U.K. singles chart, Mike Posner continues to dominate with I Took A Pill In Ibiza, racking up his fourth week in pole position.
Sia's Cheap Thrills featuring Sean Paul, and Fifth Harmony's Work From Home place at two and three, respectively.