The Scottish champions had attempted to sign the Swedish striker on Monday, but a failure to lodge paperwork with the Scottish Professional Football League (SPFL) by the 11pm transfer deadline appeared to have halted the move.
However, Celtic have now been granted permission to complete the deal.
"Delighted to have finally joined @celticfc on loan... Can't wait to get started and play in front those fans #TheBhoys," Guidetti tweeted.
The 22-year-old joined City at the age of 16 and has been shipped out on a number of temporary deals in recent times.
Following a brief spell at Burnley during the 2010-11 campaign, Guidetti scored 20 goals in 23 league appearances for Feyenoord the following season.
Guidetti came off the bench six times for Stoke City last term, but will hope to feature more regularly under Ronny Deila.
He joins a Celtic frontline that also saw the addition of Serbia international Stefan Scepovic on Monday, and follows Craig Gordon, Jo Inge Berget, Aleksandar Tonev, Jason Denayer and Mubarak Wakaso in making the move to Glasgow for the new campaign.
