Fobbs will receive a $195,000 annual salary. The board unanimously agreed to his selection and praised the hiring, which university leaders hope can improve a tense relationship between the school's administration and players.
Currently the tight ends coach at McNeese State, Fobbs will remain with McNeese through the Cowboys' second-round FCS playoff game Saturday. He'll then take over at Grambling, where he played in the mid-1990s for Hall of Fame head coach Eddie Robinson.
"Woven to me in my heart is Grambling State University. Flowing through my veins is black and gold," Fobbs told the board, choking up as he talked about his new job.
Grambling won only one game this season, a year likely to be remembered most because a player walkout forced the cancellation of Jackson State's homecoming game in October. Players said they were protesting decrepit training conditions, long bus rides to Kansas City and Indianapolis and the administration's handling of the once-proud program.
University leaders said the school received more than 100 applications for the coach's job despite the upheaval on campus.
"I plan to hit the ground running and working hard to build a program that is successful and to get Grambling back to the way it has always been," Fobbs said.
Before working at McNeese, Fobbs also had been an assistant coach at Northwestern State. He'll take over at Grambling for Dennis "Dirt" Winston, who was the school's second interim coach of 2013.