The news comes after micro-engraver Graham Short was spotted in Bath last month, prompting speculation he had spent it in the city.
Mr Short told BBC Radio Bristol he would presenting it to Bath's Jane Austen Centre as a framed gift.
He said it would mark the 200th anniversary of the author's death.
Mr Short, who lives in Birmingham, said he originally visited the centre to learn more about Jane Austen as felt he "really ought to know more about her life than I do".
He added he would be returning to Bath on 18 July to hand over the engraved note.
He said: "It will be framed with glass on the back and the front so you can see through it."
David Lassman, from the centre, said it is currently in discussion over how best to display it.
He added: "We're overwhelmed with the gift, which we hope will raise the centre's profile.
"It's particularly poignant it will be presented on her anniversary."
Mr Short initially engraved 5mm portraits of Jane Austen on four £5 notes, making each worth thousands of pounds.
One of the four notes was spent in a cafe in Blackwood, south Wales, the others somewhere in England, Scotland and Northern Ireland.
So far, three have been accounted for.
Jane Austen was an English novelist born in 1775 whose books were set among the English middle and upper classes.
A fifth £5 note engraved with a tiny portrait of author Jane Austen will not be going into circulation, the artist behind the project has said.