In September of last year, Cobos pleaded guilty to conspiracy.
He was accused of receiving $4,500 in bribes from lobbyists in exchange for his vote as the head of the El Paso Commissioners Court.
Aguilar also pleaded guilty to conspiracy after being accused of bribing Cobos while he was county judge.
"I come to you with a heavy heart," Aguilar said before apologizing to the U.S. and his family for the damage he had caused.
Both men will be allowed to surrender to the Bureau of Prisons on February 11.