The deadline for applications is the beginning of January, and interviews will take place in Whitehall in the last week of the month.
DEXEU is likely to pay between £70,000 and £90,000, with the recruit overseeing a team of 45, although slightly more than half of these are Freedom of Information and ministerial correspondence staff, leaving a comms team of around 20.
The role is currently held on an interim basis by Rae Stewart, who was comms chief at the Department of Energy & Climate Change for nearly two years before joining the newly created department in July.
Stewart is understood to be considered a strong candidate for the role, which is a two-year fixed term appointment, the candidate information pack says. The hire will be made through Civil Service Resourcing, rather than an external recruitment agency.
Victoria Dean recently joined Portland Communications as a partner, having worked in a number of Foreign Office roles, and most recently spent a short period working in DEXEU.
She said: "I think the department is an unusual one, because it is new and has grown and is still needing to grow. It's not an easy place to work but it is, unusually for government, quite entrepreneurial in its approach."
"While it is an unusual government department, I think the skillset is perhaps no different from [that needed] at other government departments, other than the fact that there is such a huge level of interest, and handling a 'no running commentary' position as a comms person is difficult to do."
Simon Petar, associate director at iNHouse Communications, whose co-founder left in the summer to become Theresa May's spokesperson, said: "This is the biggest communications gig in Whitehall and whoever gets it will need the patience of a saint, the strategic brilliance of a chess grandmaster and the ability to inspire confidence in Ministers and an army of PRs.
"Ensuring the Government’s narrative flows seamlessly to all corners of the UK in a concise and timely manner is an enormous challenge, especially given everyone from Holyrood to the Dog and Duck will have an opinion."
Alex Deane, MD of public affairs at FTI Consulting, who also ran the Grassroots Out! campaign group during the EU referendum, said: "Whilst many Brexiteers will instinctively feel more comfortable if this is a political 'believer' rather than a civil service lifer, that isn't really the most important thing - the ability to deliver the department's message and build a close relationship with the ministers and key press stakeholders is the vital thing."
Deane described the role as "one of the most important jobs in present-day comms".
"Whoever is appointed needs to be able to explain complex concepts in approachable language, hold a dozen different strands of thought in his or her head at once, command the respect of the press and the trust of experienced ministers, and be willing to work exceptionally hard for a couple of years pretty much without letting up. It's no small challenge," he said.