The Lincolnshire stalwart departs on 22 August following a number of rocky years at the authority, which has seen the jailing of former leader Jim Speechley in 2004 and the departure of leader Ian Croft last year after allegations of misconduct.
The communications arm at the authority is being reviewed as part of a council-wide shake-up, following threatened intervention by the Government last year (PRWeek, 14 July).
Jackson's PR manager role will be superseded by a head of comms and community post, for which the council will recruit in September.
The successful candidate will report to assistant chief executive Marcus Coleman, to whom Jackson currently reports.
"My role does not exist in the revised comms structure, which gives me an opportunity to take redundancy," he told PRWeek.
The new structure has not yet been finalised, but it will centralise comms staff, with a team of four operating within social services, according to the council.
The team will be expanded, but it is not known by how many, said Jackson.