The Faculty of Divinity said an initial invitation to the psychology professor had been rescinded following "a further review". Some students had protested against the visiting fellowship.
A controversial figure, Prof Peterson has attracted attention for his outspoken views on gender, race, political correctness and climate change.
In a response published on his website, he said: "I think the Faculty of Divinity made a serious error of judgement in rescinding their offer to me."
Prof Peterson had previously said he was looking forward to spending two months at the university, as part of plans to produce a lecture series about the biblical book of Exodus.
The 56-year-old, who has previously taken part in Premier's Unbelievable show, said he had been in talks with the Faculty of Divinity about giving talks to students which would have been of "mutual benefit" to all parties concerned.
Jordan Peterson requested a visiting fellowship at the Faculty of Divinity, and an initial offer has been rescinded after a further review.— Faculty of Divinity (@CamDivinity) March 20, 2019
The Faculty said: "Jordan Peterson requested a visiting fellowship at the Faculty of Divinity, and an initial offer has been rescinded after a further review."
A spokesperson for Cambridge University was quoted by the Guardian as saying: "[Cambridge] is an inclusive environment and we expect all our staff and visitors to uphold our principles.
"There is no place here for anyone who cannot."
Meanwhile, the withdrawal of the visiting fellowship was welcomed by the Cambridge University Students' Union.
In a statement seen by the newspaper, the Union said: "We are relieved to hear that Jordan Peterson's request for a visiting fellowship to Cambridge's faculty of divinity has been rescinded following further review.
"It is a political act to associate the University with an academic's work through offers which legitimise figures such as Peterson.
Will be handing back my @Cambridge_Uni degree (double first, modern history) in protest of rescinding Jordan Peterson's fellowship. I had plenty of good memories while studying for my degree, in which I obtained a double first. But my commitment to free speech is much greater— hussein kesvani (@HKesvani) March 20, 2019
"His work and views are not representative of the student body and as such we do not see his visit as a valuable contribution to the University, but one that works in opposition to the principles of the University."
In his response, Prof Peterson continued: "In the fall, therefore, I will produce the lectures I plan to produce on Exodus, regardless of whether they occur in the UK or in Canada or elsewhere, and they will attract whatever audience remains interested.
But why was such an offer offered in any case? For so many reason, this man is deeply problematic.— Dr H.A. Hellyer (@hahellyer) March 20, 2019
"But I think that it is deeply unfortunate that the authorities at the Divinity school in Cambridge decided that kowtowing to an ill-informed, ignorant and ideologically-addled mob trumped participating in an extensive online experiment in mass Christian and psychological education.
"Given the continued decline of church attendance, the rise in atheistic or agnostic sentiment, the increasing irrelevance of theological education and the collapse in interest in such matters among young people, wiser and more profound decisions might have been made."
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