The star, now 29, made around 20 copies of the album, called Spinning Man.
He previously admitted he did not want anyone “get hold of a copy” so he has 19 in his possession.
Now one of the demos, which features songs with titles like Addicted and Misery, has been unearthed from a drawer where it had been “forgotten” for many years.
Sheeran was staying with relatives and sleeping on their sofa, while making money by busking, when he handed a copy to a friend of the relatives.
The man’s brother, Kevin, 48, who does not want to give his surname, is selling the CD.
“My brother put it in a drawer and forgot about it,” he told the PA news agency.
“At the time Ed Sheeran was this just this wee, ginger-haired busker and he thought nothing of it. He didn’t realise he would go on to be one of the world’s biggest pop stars.”
In his book, Ed Sheeran: A Visual Journey, the star, who now has an estimated fortune of more than £200 million, said he wrote the songs after his first love left him heartbroken.
“In 2004, I made my very first album, Spinning Man, named after a picture that my dad had,” he said.
“I burnt the CDs myself and made the covers. There were 14 songs, and they were all songs that rhymed.
“One lyric went: ‘I’m a typical average teen if you know what I mean’.
“There are probably 20 copies of Spinning Man in existence, and I have 19 of them. I don’t want anyone else to get hold of a copy.”
Sheeran added: “Most of the songs were about a girl called Claire. She was my first love when I was 13.
“It was a very innocent love, and we only ever held hands, but it lasted a fair amount of time. Then came my first devastating break-up.
“Looking back, it really wasn’t that bad, but at the time it was soul-shattering. When she left me, I wrote a lot of songs off the back of it – my first love songs.”
Kevin said he was impressed when he heard the CD.
“The quality of the songs are really good and I was shocked by how good he was on the electric guitar. It does sound like Eric Clapton at moments.
“I play guitar. The fact that he was playing like that when he was 13, he must have been talented from the start.”
He said the songs “express teenage love and loss, frustration and longing”.
The CD features cover photography by Sheeran’s father, and is expected to fetch £10,000 at Omega Auctions.
Kevin added: “Most of the other CDs – or all the other CDs, as far as I know – have a sticker on the disk, saying ‘Ed Sheeran Spinning Man’.
“But for this one he’d run out of stickers so he wrote his name on the disc and handed it to my brother. So it might be the only signed copy.”
Auctioneer Paul Fairweather said: “We’re really excited to have the chance to sell what’s now an important artefact in contemporary music history, a milestone in the development of one of the world’s biggest pop stars.
“We’ve no doubt it will attract worldwide attention.”
