The singer started a diploma at the Academy of Contemporary Music in Guildford, Surrey, in 2009 but gave it up as his musical career took off.
A letter formalising his resulting failure was sent to him a year later.
It is on show at Christchurch Mansion, Ipswich, along with other personal objects and memorabilia.
Sheeran's father, John, has curated the Ed Sheeran Made In Suffolk exhibition, which opens on Tuesday.
