Experienced centre-half Kelly joined the Killie squad at training this week after former Hearts and Livingston boss John Robertson, now in charge at the League of Ireland side, gave Jefferies a glowing report.
The 28-year-old Irishman has had spells at Carlisle and Portadown before a second stint at hometown club Derry.
Jefferies said: "He was recommended to us by John Robertson and he looked good on his first day with us on Tuesday.