Hundreds of fans queued up outside the store in Barker's Pool to buy rare and exclusive merchandise, and of course the hotly anticipated new album Tranquility Base Hotel & Casino, which is also released today.
The Steel City store is one of just six pop-up shops around the world - the others being in New York, Sydney, Paris, Berlin and Tokyo.
Joe Goodwin, aged 22, and Emily Currie, aged 21, of Leeds, camped outside the shop through the night to make sure they were first in line.
Emily said: "It was freezing. People were coming up to us and asking if we were alright. They thought we were homeless!"
Joe added: "We are massive fans though and it was all worth it. We got some amazing stuff."
There has been speculation that the band - which formed in High Green in 2002 - might make an appearance at the shop themselves sometime this weekend as they are not due to play live again until May 22 in Berlin.
But for the time being fans are just happy to be able to hear the band's first new songs since 2013's AM album.
Joe said: "I think it's unlikely that they'll come. But we're going to see them live later this year anyway. And I love the new songs."
Inside the store fans were treated to a video showing the band making the album in the studio as songs from the LP played out over speakers.
Many were excited to get their hands on gold vinyl copies of the album.
There are only 2044 of them available and they are only available in Sheffield.
The vinyl versions at the five other pop-up shops are only available in silver.
Ashley McLoughlin, aged 22, and Jack Brothers, aged 19, travelled over from Preston and stayed overnight in a hotel to make sure they got near the front of the queue.
Ashley said: "We got here at 5.30am and there were plenty of people here then. The gold vinyl looks great though.
"We've been listening to some of the new songs. Four out of Five is my favourite so far."
He said that he spent about Â£90 on merchandise.
"But that's what you work for. It was all worth it," he added.
Jack said: "The shop looks great inside. It's like an art exhibition."
The Sheffield shop will be open today from 8am to 5pm, Saturday 9am to 5pm and Sunday 10am to 4pm.
The band will play four homecoming shows at the Fly DSA Arena on September 18, 19, 21 and 22 later this year as part of a wider UK tour.