Campbell played 291 games for the Tigers before retiring in 2005 and was a four-time club best and fairest winner.
He had held various off-field roles at the Western Bulldogs and Richmond.
Gieschen was the umpiring director for 14 years before resigning last month.
"What attracted me to the role was working in a high-performance environment where I think I can make an impact," Campbell said in a statement.
"The breadth of management skills required in the implementation of the national umpiring plan is an area that excited me and I want to continue the good work already done in increasing the respect for umpires and help boost the number of umpires at grass roots level."
Umpires coach Rowan Sawers also resigned in late October after 16 years in the role.
Former field umpire Hayden Kennedy has taken over from Sawers.