Fobbs, whose hiring was announced Wednesday, will remain with McNeese through the Cowboys' second-round FCS playoff game Saturday. He'll then take over for Dennis "Dirt" Winston, who was Grambling's second interim coach of 2013.
The 39-year-old Fobbs was a Grambling running back under the late Hall of Fame coach Eddie Robinson. He also has been an assistant coach at Northwestern State.
"It's an opportunity I've always dreamed of at a place where I've always dreamed of being," Fobbs said. "I stand on the shoulders of a number of great men, and many of them coached and mentored me. They instilled in me the importance of GSU's expectations, history and legacy and we're going to do just what they expect and deserve."
Grambling closed a school-worst 1-11 campaign with a 40-17 loss to Southern in the Bayou Classic last Saturday.
"I couldn't be happier that Broderick has agreed to return home and lead our football program back to greatness," Grambling president Frank Pogue said. "It's obvious that we've had a couple of truly difficult seasons, and that's not something that Grambling State alums and supporters are used to -- and we're about to change that with Fobbs."
The season will be most remembered for a walkout by players in protest of decrepit training conditions, long bus rides to Kansas City and Indianapolis, and the administration's general handling of the once-proud program.
Players were particularly upset over the early-season firing of popular former head coach Doug Williams, who is one of the school's best known alumni, having won a Super Bowl with the Washington Redskins. They portrayed the firing as symbolic of the administration's dysfunctional relationship with some of its best-known former players and other alumni or prospective donors who had the means to address the football programs' needs expediently.
Williams was replaced by George Ragsdale, who lost five games before being replaced by Winston during the same week in which the walkout was staged.
The walkout lasted about a week resulted in Grambling forfeiting Jackson State's homecoming game.
When players returned, they rallied around Winston, a former NFL linebacker and former assistant under Robinson in the 1990s. In Winston's four games, the Tigers won for the only time and lost a pair of close games before falling in the Bayou Classic.
Winston said openly he was interested in getting the job permanently, but was under the impression the university may have other plans.