[4] The album features guest vocals from Elly Jackson of La Roux, Iggy Pop, and Brandon Flowers of The Killers.

[5] This is the first album without former bassist Peter Hook, as well as the recorded debut of Tom Chapman and the return of Gillian Gilbert, who had taken leave from the band in 2001, but toured with them from 2011 onwards.

[6][7] On 2 and 4 September 2014, Billboard, along with Stereogum and Consequence of Sound reported that New Order had signed on to Mute Records and that future releases were expected, at the time planned to be EPs which would then be "probably put together as an album."

[18][19][20][21][22][23] Music Complete was released on 25 September in five different formats: CD, regular and limited-edition double-clear LP, digital download, and an 8-piece deluxe vinyl box set.

[1] Barry Walters of Rolling Stone wrote: "Just as Curtis' suicide inspired his bandmates to reinvent themselves as New Order in 1980, Hook's departure frees them to create their most varied and substantial work in decades.

"[33] Michael Roffman of Consequence of Sound called Music Complete "the rare late era LP that blossoms with life, while also echoing the past",[35] while Tim Jonze of The Guardian wrote that the album "feels like the freshest thing they've done in ages.

"[31] Stephen Dalton of Uncut felt that it "drags and trundles in places", but is "easily New Order's best album since Technique, and probably their most musically diverse ever.

"[34] In a less favourable review, Tim Sendra of AllMusic called it "a watered-down and uninspired album by a band that lost the plot long ago and can now only capture an occasional glimmer of what made it so great in the first place.

"[26] Concluding a less favourable 1 of 5 star review, Truck & Driver wrote: "...full of soggy, uninspired self-indulgent material that sounds like a mish-mash of 80s B-sides.