Former Dewsbury Rams, Wakefield Trinity and Ireland coach Kelly, 58, has been at John Smith’s Stadium in his current role since 2014.
He has played a major role in successfully bringing talented youngsters such as Kruise Leeming, Darnell McIntosh and the Senior twins into Huddersfield’s first team.
After another poor season overall at Super League level, however, the West Yorkshire club’s hierarchy has conducted a review to try and improve matters in 2020.
Kelly - who acted as Giants' interim head coach following Paul Anderson's sacking in 2016 - will now combine his roles and take on extra responsibilities.
Huddersfield managing director Richard Thewlis explained: “Andy is highly respected throughout our club and the game at large.
“In reviewing our season with Simon (Woolford) it became apparent too much of his time was spent on matters that could be best dealt with by Andy who was in turn looking to widen his involvement with the first-team to more than just matchdays.
"The role of Rugby Manager is a natural fit for Andy and will enable more hands-on coaching and conditioning time for all the first-grade staff and take away their administrative and logistical burdens which, whilst being vital for the smooth running and optimisation of the club, it is felt are best sat on Andy's desk.
"We have already said that we will do all we can off the field to impact what occurs on it and this is the first of a number of announcements that we expect to make in the coming weeks as we reshape on and off the field under Simon’s guidance.”
Kelly, who represented England during his playing days as a second-row with hometown Wakefield and Hull KR, said: “I think this is a role that we need going forward to improve at the top level and its one that I am looking forward to getting stuck into.
"The logistical side of running clubs is frankly huge and things don’t happen without planning, administration and then action of course which I’m keen to get stuck into ahead of the planned return to train date in mid-October.
"I will still be overseeing all aspects of the academy now that we have got our structures, staff and procedures in place which I like to think are running well although we will have some modifications with the advent of reserve grade rugby and lowering of the upper academy age to work through.”