The award, organised by the Scottish Poetry Library (SPL), is given for a collection by a poet aged 30 or under, "of Scottish birth, formation or residence", and consists of a grant of £20,000 plus support for publication if the poetry collection is as yet unpublished.
Claire Askew, Niall Campbell, Tom Chivers, Harry Giles, Stewart Sanderson and Molly Vogel have all been shortlisted for the award.
The judges Stewart Conn and Jen Hadfield said in a statement: "This award represents significant and deserved recognition for the shortlisted poets.
"We think Edwin Morgan would have been thrilled by the new Scottish poetry that his generosity honours and invests in today, and that he might have been tickled to recognise the legacy of his own boundless experimentation in some of the poems."
The winner will be announced at an event at the Edinburgh International Book Festival on August 16, chaired by Jackie Kay, with readings by the shortlisted poets.
Professor James McGonigal, on behalf of the trustees of the SPL, said: "Edwin Morgan always looked towards a positive future, for humanity generally, for Scotland in particular and for poetry.
"At the end of a life of astonishing creativity, that positive outlook was carried forward by his plan to support young Scottish poets through a generous prize fund that would recognise and release their talents."
The judges are Scottish poet and playwright Stewart Conn, Edinburgh's inaugural Makar, and Jen Hadfield, based in Shetland, whose collection Nigh-No-Place won the TS Eliot Award in 2008. Poet and scholar Meg Bateman was the Gaelic adviser.