Cox, 49, denies the allegations and is fighting the dismissal.
The university confirmed Cox's departure. It said an independent disciplinary panel had met to consider "a variety of allegations against Professor Cox".
The panel found Cox had "committed serious breaches" of financial regulations and procedures, data protection requirements and the university's duty of care towards a member of staff. It was not satisfied with Cox's explanations.
"Given the evidence presented, the seriousness of these findings, and all the circumstances of the case, the university has accepted the panel's clear recommendation to terminate Professor Cox's employment."
The university said Cox had the right of appeal. He told the Herald on Sunday from London he "strenuously denied" the allegations and would appeal.
"It has not been logged yet but it will be soon by my lawyer. I expect the hearing will be months rather than weeks but I will have to wait."
Cox said he had not made a decision about returning to New Zealand.
He holds degrees including Master of Law and Doctor of Philosophy. He also has a Master of Arts in ecclesiastical law from the Archbishop of Canterbury's Examination in Theology and a Licence in Theology from the University of Wales.
Two years ago he was ordained a deacon in the Anglican Church in Wales and became a non-stipendiary assistant curate in the parish of Llanbadarn Fawr on the outskirts of Aberystwyth. He became a priest last year.
Hywel Jones, former vicar at the local parish church St Padarn's, said the dismissal had come as a shock to the community.
"When we found out three weeks ago, we had to stop him taking services.
"People start talking and it was a difficult position so we had to act. Of course, it's all subject to an appeal so we'll have to see the outcome but I think it's going to be very difficult for him to return to the law after what's happened. Maybe he'll return to New Zealand."
Cox has featured in New Zealand media commenting on everything from intellectual property in fashion to the selection of the Governor-General.
He trained as a lawyer in the 1990s before becoming a law professor at AUT.
In 2009, Cox was ordained in the Diocesan Training Programme at Holy Trinity Cathedral in Parnell.
He was once chairman of the Monarchist League of New Zealand.