Omogrosso was outrighted last week along with right-hander Ramon Troncoso, as well as catchers Bryan Anderson and Miguel Gonzalez, as the White Sox looked to clear 40-man roster space for potential offseason acquisitions.
Omogrosso pitched in just 12 major league games this past season, posting an 0-2 record with a 9.37 ERA. He has a career 5.54 ERA over 39 big league appearances.
Septimo did not pitch in the major leagues in 2013. He had a 5.02 ERA in 21 relief appearances with the White Sox in 2012.
Gimenez had just 68 at-bats over 26 games before he was designated. He batted .191 with two home runs and 10 RBIs.