Vic Haines has listed the bike, valued at £10,000, on the online auction site in what is the latest twist in a bitter 20-year dispute between the pair.
The model is almost identical to Obree's self-built "Old Faithful", on which he twice broke the record for the greatest distance cycled in one hour.
Mr Raines was sacked by Obree shortly after his success in 1993, and he claims he was left £45,000 out of pocket.
The businessman, who is also a competitive cyclist, said he could no longer bear to look at the bike.
He said: "This bike is the Rolls Royce, the best you can get. I kept it and put it on the wall, I removed the chain and the wheels and it became a piece of objective art.
"But it eventually got to me and two weeks ago I thought to myself, 'I can't keep looking at that'. It has haunted me for the last 20 years. I know I am never going to get my money and the bike reminds me of that, so I decided to sell it."
The bike was made by London-based cycle shop Shorter Rochford.
Obree used it in Hamar, Norway, on July 16, 1993, during his attempt to break the record of 51.15km, set by Italian Francesco Moser, nine years earlier.
But after failing the challenge, he returned the next day and cycled 51.59km using his original "Old Faithful" bike.
Obree, who lives in Prestwick, Ayrshire, said yesterday that the bike was of very little importance, and denied he owed money to Mr Haines.
He said: "I was hoping I would not have to go into all this. I have learned humility and to let go what you can let go. If he makes a few quid out of selling the bike, I have no problem with that."