But he faces strong competition from grime artists Stormzy and J Hus and rapper Loyle Carner, who each receive nominations for their debut albums.
Their nominations come a year after Skepta took home the Â£25,000 prize, beating bookies' favourite David Bowie.
Former winners The xx and Alt-J also make the 12-strong shortlist.
Sheeran's nomination stands out because the Mercury Prize rarely recognises mainstream pop.
In recent years the likes of Adele's 25 and Sam Smith's In the Lonely Hour have been overlooked, as the prize seeks to champion new and underappreciated music.
Yet Sheeran's domination of the charts would have been hard to ignore. When it was released, all 16 of Divide's songs made the Top 40.
The album has sold 2.06 million copies in the UK, making it the year's biggest-seller.
The full list of nominees is:
Read more about the shortlist and watch videos of the artists on BBC Music
The shortlist was chosen by a panel of judges that includes Marcus Mumford, Jessie Ware, Radio 1's Clara Amfo and jazz musician Jamie Cullum.
Among their selections are two albums that tell short stories about fictional characters.
On Let Them Eat Chaos, poet Kate Tempest portrays the lives of seven sleepless citizens on one South London street.
In How To Be A Human Being, meanwhile, Oxford band Glass Animals turn their eye to America with lyrics loosely inspired by people they met on tour.
Many of the other nominees have written about family, with Stormzy and J Hus both dedicating songs to their mothers.
Sheeran, meanwhile, closes his album with the touching ballad Supermarket Flowers, which reflects on the death of his grandmother and its effect on his family.
Notable omissions from this year's shortlist include Rag 'N' Bone Man's Human, Wiley's Godfather and Marika Hackman's I'm Not Your Man.
Three-time nominee Laura Marling was also overlooked, despite rave reviews for her latest album Semper Femina.
The winner will be announced at a gala concert at London's Eventim Apollo on 14 September.
A controversial scheme, which saw six of the nominated albums "eliminated" at the start of last year's ceremony, has been ditched for 2017.
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Ed Sheeran has picked up his first nomination for the Mercury Prize, recognising the overwhelming success of his third album Ã· (Divide).