Ulster Bank said the more durable polymer notes, due to replace existing paper notes issued in Northern Ireland, were the result of a consultation with experts and members of the public.
The unusual currency will be legal tender across the UK.
While only the Bank of England can issue new cash in England and Wales, seven banks can do so across Scotland and Northern Ireland.
Each note will have security features to prevent fraud but separate designs under the theme Living in Nature.
The bank said the £5 note highlights “the importance of the sea and migration” in Northern Ireland and features Strangford lough and Brent Geese.
The £10 version focuses on agriculture and heritage. It contains images of Lough Erne, the Irish hare, Guelder-rose shrubs and an Ulster Glade potato.
Richard Donnan, head of Ulster Bank in Northern Ireland, said: “Innovation is at the core of our bank, whether that’s through digital technologies, in our face-to-face services, or these designs.”
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Bermuda and Kazakhstan are two territories currently using vertical banknotes.
Ulster Bank said it was working with stakeholders to ensure a smooth transition to its vertical versions from early 2019.