Edmondson ended last season as caretaker boss, with the Mintcakes given a reprieve from relegation from the EVO-STIK League West Division due to the resignation of Colwyn Bay.
Keith Singleton has been appointed as first team coach.
Club chairman, George Gudgeon, said: "I am delighted that Steve and Keith are on board, I together with the management committee have had a number of discussions with them and they are fully behind and support the new infrastructure we are putting in place, a structure that will provide a pathway for our youth and reserve team players.”
Meanwhile, Kendal have announced their pre-season programme.
Tuesday July 2: Furness Rovers v Kendal Town XI
Sunday July 7: Millom v Kendal Town XI
Wednesday July 17: Kendal Town v Morecambe
Saturday July 20: Kendal Town 1st XI v Cleator Moor Celtic (1pm Kick Off)
Saturday July 20: Kendal Town Reserves v Cleator Moor Celtic Reserves
(3pm Kick Off)
Saturday July 27: Carlisle City v Kendal Town XI
Tuesday July 30; Whitehaven v Kendal Town XI