Tickets to the star-studded show, which aims to pressure world leaders into fighting poverty, were given for free to the winners of a text lottery. But they immediately started appearing on eBay for hundreds of pounds.
"I am sick (about) this," Geldof said in a statement. "What eBay (is) doing is profiteering on the backs of the impoverished.
"The people who are selling it are wretches. But far worse is the corporate culture which capitalizes on people's misery."
Geldof organized the July 2 concert 20 years after the Live Aid sensation that raised money to help the starving in Ethiopia.
Rather than raise money, the 2005 concert aims to raise the profile of African poverty and influence the G8 group of industrialized nations, which meets in Scotland in July.
Four other concerts will be held around the world on the same day.
Performers for the London concert include, Paul McCartney, Coldplay, Madonna and REM.
Over 2 million text messages were sent in a bid to get hold of tickets, and concert organizers notified the winners on Monday.
eBay could not be reached for a comment, but the Daily Mirror newspaper quoted a company representative as saying the auctioneer is selling the tickets because "we live in a free market where people can make up their own minds."
The newspaper said eBay had offered to donate about $1.81 (one pound) for every pair of tickets sold, but the singer had rejected this, saying it was not in the "spirit of the event."