Kloess, 27, was a combined 6-3 with a 2.69 ERA last season between Double-A Birmingham and Triple-A Charlotte. He struck out 70 and allowed 62 hits in 73 2/3 innings, limiting batters to a .225 average.
Last week, the Padres designated Tekotte for assignment. He hit .163 in 49 at-bats for the big league club over the last two seasons. He spent most of the 2012 season with Triple-A Tucson.
Kloess was originally signed by the White Sox as a Minor League free agent in 2009. He's 17-10 and has a 2.39 ERA in 267 innings over the past four seasons with a low 90s fastball and what are regarded as good secondary pitches.
Kloess attended Florida Atlantic University and is a graduate of St. James High School in Plant City, Fla. He will turn 28 on Dec. 9.
Because Kloess wasn't on the White Sox 40-man roster, he won't need to be added to the Padres' 40-man roster.