The two clubs have agreed the prices hoping it will lead to a healthy attendance on Wednesday, September 24th (KO 19:45).
Swindon club spokesman Chris Tanner said: "It has been some time since our fans have seen their team take on Premiership opposition.
"Hopefully these prices will encourage fans to make the trip to Leeds and give the team their backing."
Tony Norris, spokesman for the Swindon Town Supporters' Trust, said: "I think the prices are more than reasonable.
"You would struggle to get into a Second Division match for £10, never mind a Premiership ground.
"I'm sure part of it is that the visit of Swindon might not be seen as a particularly big draw in Leeds.
"From this end, though, I'm sure it will encourage our fans to make the trip and hopefully lead to a good following at Elland Road.
"The Carling Cup is not seen by all the Premiership clubs as the biggest competition. But I'm sure the tie has added spice because there is no way Peter Reid is going to want Andy King getting one over on him."
Leeds intend to close the East upper and the South East Corner and Swindon supporters will be located in the South stand.