Hudson, who works closely with Secretary of State for Constitutional Affairs Lord Falconer, joins the Foreign & Commonwealth Office in October as director of comms.
He moves after two years at the DCA and replaces John Williams, who quit three months ago (PRWeek, 8 June).
Hudson will be supported by deputy director of comms Tom Hoskin, who will manage the media and other comms teams.
Hudson will report directly to Beckett, who recently topped a survey in Forbes magazine of the most powerful women in Britain.
DCA head of strategic comms Sue George will be acting director of comms after Hudson's exit.