He joins United after working as a scout for ex-England boss Sven Goran Eriksson.
Carlisle born Geddis has also worked with Leeds head coach John Carver at Newcastle United.
Kevin Blackwell told the club's official website: "I always felt the coaching ability needed to be improved and we now have four pro-licence coaches which puts us up there with the best in Europe. We are well stocked with quality coaches.
"David comes with a good reputation. He's a technical coach with a great pedigree.
"He's got a good reputation for developing young players and bringing them through to the first team, through his work at Middlesbrough and Newcastle.
"I want a coach who can work with the youngsters and push them through quicker. John also knows him and has worked with him. That's a help because David knows people at the club and won't have to spend too much time finding his feet."