Orgeron had previously said that Rosenthal had the potential to be a first-round NFL draft pick.
But the offensive lineman struggled to stay on the field during his time in Baton Rouge. He left school briefly last year, missing spring practice. He returned and was then suspended indefinitely in October.
Rosenthal was later reinstated and wound up starting five games last season.
He entered the portal on Monday.
"He had some personal situations that he had to take care of," Orgeron told ESPN Baton Rouge on Tuesday. "It was a hard decision, but we wish him the best. We're going to miss him."
Rosenthal's departure clears the way for Cam Wire to take over as starting left tackle.
Wire started at the position when Rosenthal was suspended last season.
"Cam's done a great job," Orgeron said. "He was the sixth player going in last year. But guys have to step up. ... I don't know who's the second left tackle, to be honest with you.
LSU is scheduled to open the season on Sept. 4 at UCLA.