Veritiero was promoted to the role last August when he was charged with leading the Future Proofing Kier cost savings programme.
His role will not be replaced and will now be assumed by chief executive Andrew Davies and chief financial officer Simon Kesterton.
A trading update to the city this morning said Kier was on course to reduce staff numbers by 1.200 by next June alongside annual cost savings of £56m in the financial year ending 30 June 2021.
Kier confirmed it is selling its historic headquarters at Tempsford Hall.
It is also selling offices at Foley Street in London and is outsourcing its IT and fleet management activities.
Davies said: “We continue to build the foundations for the future of the Group through the execution of our strategic priorities.
“Our core businesses are performing in line with our expectations and we continue to win work from a number of our major clients, whilst significantly reducing the Group’s overheads and costs.”