The verses, which end "Come all ye', the country says/You win me, who take me most to heart", will be inscribed on the timber ring beam at the top of the 1960s rotunda at the site.
The National Trust for Scotland and Historic Scotland, working with Creative Scotland and the Scottish Poetry Library, commissioned 10 Scottish poets to write about the site and the surrounding landscape and asked the public to vote for their favourite.
Almost 1000 people voted, and Jamie's poem won by a clear majority.
The judges of the prize, including Scots Makar Liz Lochhead also deliberated on the poems, and came to the same conclusion.
The commission is part of the Battle of Bannockburn project to upgrade the heritage site which is a place of commemoration.
The new facilities will include a visitor centre with state-of-the-art interpretation of the battle and a programme of conservation, restoration and enhancement of the commemorative park and its flagpole, Bruce statue and Rotunda monuments in time for the 700th anniversary of the battle in 2014.
Also an essayist and travel writer, Jamie is professor of creative writing at Stirling University.
Ms Jamie said: "From the start I wanted this piece of work to make a nod to the Scottish literary tradition.
"More than a nod – a profound bow. Because Barbour, Burns and Scott had all written about Bannockburn, and had all done so with a four-beat line, I decided my piece would be in tetrameter too, as a homage."
Liz Lochhead said: "One of the great difficulties in composing poetry on a national theme is to avoid what sounds like a slogan – slogans are the enemy of poetry. Kathleen Jamie's poem impressed me with its clarity and condensed language."