We British: An Epic In Poetry will run throughout the day on 8 October.
Marr will oversee a series of readings illustrating how poetry of the past reflects the issues of today.
"Ripping up Radio 4's schedules for National Poetry Day seemed a rather bold and brilliant thing to do," said the broadcaster in a statement.
Poems selected for the day-long project include Walter Raleigh's The Lie, which rails against corruption in the church and state; and William Dunbar's Lament for the Makars, a roll-call of deceased poets, starting with Chaucer.
The works of William Shakespeare, William Wordsworth, Christina Rossetti and Ted Hughes will also feature, as well as verses from less familiar figures such as Anne Askew and Anne Bradstreet, and anonymous writers of medieval ballads.
"I can't remember British history being told, in this way, through the directness of poetry," said Marr.
"But if we want to get a real sense of what life was like in early medieval England, or how people felt about the plague or the fanaticism of the wars of religion; or the trauma of the slow decline of religion during the arrival of science, then the witness offered by great poetry is a very good way in.
"If there is a single art which the people of these islands have excelled at, beyond all others, it is surely poetry."
Among those joining Marr to read and discuss the poems will be Charles Dance, Harriett Walter, and poets Gillian Clarke, Michael Rosen and Daljit Nagra.
Sprinkled throughout the day's schedule on Radio 4, it will amount to six hours of broadcasting, culminating in a live poetry and music performance at 22:45 BST.
Andrew Marr, Dominic West and Fiona Shaw will mark National Poetry Day by telling the story of Britain through its poetry on BBC Radio 4.