English champions City and Celtic soon confirmed that Guidetti had joined Ronny Deila's side on a season-long loan deal.
Guidetti, who is on Sweden Under-21s duty, welcomed the news.
He wrote on his Twitter account: "Delighted to have finally joined @celticfc on loan ... Can't wait to get started and play in front those fans @TheBhoys"
The striker arrived at Celtic Park on Monday evening but the club only announced the signing of Serbia striker Stefan Scepovic before the deadline.
Celtic successfully persuaded the Scottish Professional Football League to extend its deadline from 11pm to midnight, to fall in line with the SFA's deadline.
But part of the registration document was received just after midnight, forcing the SFA and SPFL to take the club's case to FIFA.
The bureaucratic hitch might yet prevent Guidetti playing in the Europa League group stages as the deadline for the submission of squads was midnight on Tuesday.
Guidetti is looking to rejuvenate his career after injury and illness derailed his progress.
He scored 20 goals in 23 games for Feyenoord on a loan spell in 2011-12 and made his full international debut, but a problem with his leg, which was caused by illness, ruled him out of Euro 2012.
He came back last season but a loan spell at Stoke only yielded six substitute appearances, with no goals.