Robinson, who guided the Trojans to the 1978 national championship and five Pac-10 championships, last coached in college at UNLV in 2004. He was a volunteer assistant at San Marcos High School in California in 2010.
"I want to welcome Coach Robinson and his wife Miss Beverly to the LSU family," Orgeron said in a statement. "Coach has been a great friend and mentor to me and he will be a very valuable resource for us in growing our championship culture at LSU."
Robinson, who was inducted into the College Football Hall of Fame in 2009, will assist Orgeron in the daily planning of practice, personnel and game planning, according to the statement.
Robinson, 83, coached USC from 1976 to 1982 and then again from 1993 to 1997. In between, he coached the Rams, leading his teams to the NFL playoffs six times, including two appearances in the NFC Championship Game.
Robinson has an overall college coaching record of 132-77-4 and an NFL regular-season record of 75-68. He went 4-6 in the NFL playoffs.
In 12 seasons at USC, Robinson guided the Trojans to a 104-35-4 overall mark. His teams went 28-42 in six seasons at UNLV from 1999 to 2004.