The youngsters have played for the Spireites in their pre-season fixtures this summer and will primarily feature for the club’s second-string sides next season.
Midfielder Donohue was most recently at Evo-Stik League Northern Premier Division side Sutton Coldfield Town while forward Orrell was at Conference club Gateshead last season.
Spireites boss Dean Saunders said: “We have a reserve team this season and they are just two players I thought I can work with.
“Whatever they can do for us right now is great, but I would imagine that in a few years we will be seeing the best of them.
“They are young lads who are enthusiastic and who have promise and they have to try to force their way into the team and make me pick them.”