The move was made possible by midfielder Stephen Ireland signing for the Potters on a permanent deal from Aston Villa.
Ireland has so far performed admirably at the Britannia Stadium, making 16 appearances under Stoke boss Mark Hughes - including nine starts - and scoring three goals.
It is the second time in their careers Ireland and Hughes have joined forces, as the 27-year-old played under the Welshman for 18 months from June 2008 to December 2009 at Manchester City.
Stoke have not revealed the length of Ireland's contract, but Stoke boss Mark Hughes said: "Stephen is a talented footballer and has shown what he's capable of since he joined us.
"We're delighted to have made his switch a permanent arrangement as it also gives us the opportunity to bring in another player on loan if necessary."
Guidetti, 21, joined City at the age of 16 but his career has been held up by injuries and illness.
He has appeared twice on the City bench this season but the club feel he would benefit from having greater opportunities elsewhere.
Hughes told the club's website: "We wanted to try and add different options to our attacking threat and John will certainly do that.
"He's someone who if you get him in the right areas will make the most of opportunities that come his way because he's a natural goal-scorer.
"There were several clubs who were interested in taking him on loan and we're delighted that he has chosen to join us."
The Potters have Liverpool's Oussama Assaidi as their other permitted loanee.
Guidetti said: "It's a dream for me to be honest, because I have always wanted to play in the Premier League, which is in my opinion, the toughest and most demanding league in the world.
"It's going to be a real challenge for me, but I have trained with the first-team players at Manchester City for a long time now, so I feel I am ready for this opportunity.
"It has been a mentally challenging time for me over the past year or so, but in times like that you are really challenged, and I feel I have come through everything pretty well.
"Now though, I am just itching to get back on the pitch and scoring goals because there is no better feeling in the world than hitting the back of the net in front of thousands of supporters."