Hill's current role of DCLG director of strategy and private office is to be expanded when Eykyn leaves the director of comms job at the end of the month for British Gas.
There is also a change of deputy director of comms, with Jane Houghton departing to join Milltown Partners and Sunday Express political editor Kirsty Buchanan succeeding her in February.
Hill joined the department in 1997 and took on his current role last October, having previously been principal private secretary to the Secretary of State Eric Pickles, while Buchanan has worked for the Sunday Express for more than seven years.
DCLG confirmed both appointments, and a department source added: "Hill taking on the role recognises the close work between his team and the comms team. It is about giving a more unified and coherent offering across the department."
The source added the pair’s efforts over the coming year were likely to be influenced by departments seeking to show that they have delivered on promises in the run-up to the 2015 general election.
They said: "In the DCLG’s case that is likely to involve, among other things, showing how it has contributed to growth in the economy, an increase in the housing supply and drives for greater efficiency in value for money for the taxpayer at local level."
Buchanan said: "After more than a decade working in the lobby I felt the time was right for a new challenge and this was an opportunity too good to miss. I am excited to be joining the Department for Communities and Local Government at a time when issues such as housing, planning and community cohesion are at the top of the news agenda."