The trio, who were locked in talks throughout transfer deadline day, have all agreed deals which will take them to the Britannia Stadium.
Gudjohnsen and Wilson were expected to be on their way to the Potters on Tuesday, having been linked with the club for some, but the arrival of Pennant came as something of a surprise.
"Manager Tony Pulis had clearly indicated that he wanted to bring in goals to his first-team squad and the signings of Gudjohnsen and Pennant, coming on top of those of Jones and Walters, fulfilled that objective on what proved to be a busy deadline day," read a statement on the club's official website.
"Pulis made a fourth signing on the day when experienced midfielder Salif Diao returned to the Britannia Stadium to sign a new two-year agreement.
"While Diao was putting pen to paper, Republic of Ireland U21 star Wilson arrived for talks about a player-plus-cash exchange deal that takes Liam Lawrence and David Kitson in the opposite direction to Championship club Portsmouth.
"Then, Icelandic international Gudjohnsen arrived for talks in the afternoon before being shown City's new £7million training facility at Clayton Wood.
"But in the final countdown to the 6pm transfer deadline, it emerged that Pulis, a long time admirer of Pennant, had managed to clinch the signing of the 27-year-old winger on a six-month loan agreement.
"City are awaiting confirmation from the FA and Premier League that the transfers of Gudjohnsen, Wilson and Pennant have gone through."