The port, which is the largest of the UK's publicly owned trust ports, has handed the agency a six-figure brief.
Fishburn won the business after a nine-way shoot-out that was said to have involved a number of major players - including Bell Pottinger Public Affairs, FD Public Affairs, Finsbury and Portland. A source involved in the pitch process said the account was worth 'well into six figures'.
The Port of Dover wants to build the largest roll-on, roll-off port in the UK. It has been looking at bringing in a potential private investor to fund the second terminal, expected to cost about £400m.
However, as a non-financial public corporation, the port would have to seek government permission to launch a debt-financed expansion and the borrowing would be added to the fast-growing overall public sector debt.
Fishburn will provide public affairs and media support, and assist with a planned stakeholder consultation exercise.
Dover Harbour Board director Tim Waggott said: 'We have ambitious plans to expand future capacity with four new cross-Channel ferry berths, and to play our part in regeneration of the town and harbour area.
'We have appointed Fishburn Hedges as part of ongoing efforts to communicate our vision for Dover to local people and to regional and national stakeholders.'