Shay was an assistant on Forbes' staff at ETSU the past five seasons. The Buccaneers went 130-43 during that time for the program's best record over a five-year stretch in school history.
ETSU went 30-4 in 2019-20, set a single-season school record for victories and won the Southern Conference's regular-season and tournament titles.
Shay said in a statement released by the university that he is "humbled, excited and thankful for this opportunity."
"I understand the expectations and standards that have been built for the men's basketball program and guarantee I am going to give my very best every day."
ETSU had been seeking a coach since Wake Forest hired Forbes on Thursday to replace the fired Danny Manning. Shay had been serving as interim coach while school officials decided on Forbes' permanent replacement.
Before coming to ETSU, Shay worked as an assistant coach at North Dakota, Northwest Florida State College, Tennessee, Milwaukee and Mercyhurst (Pennsylvania) College. He's a former Iowa walk-on.