Bolden is allowed to transfer immediately because of NCAA sanctions against the Nittany Lions football program stemming from the Jerry Sandusky child molestation scandal.
LSU, which reported for fall camp Wednesday, already has its starting quarterback spot set with junior Zach Mettenberger. However, coach Les Miles says Bolden "is talented and will be given every opportunity to compete."
Bolden, who has two years of college eligibility left and ample playing experience, likely will compete for a backup role this season with Stephen Rivers, the younger brother of NFL quarterback Philip Rivers.
A spot recently opened up for another quarterback at LSU after recruit Jeremy Liggins was unable to qualify academically and decided to enroll in junior college.
"We had a great need at quarterback" after recruit Jeremy Liggins failed to qualify academically, Miles said. "We recruited Rob several years ago and he chose Penn State. ... Two or three months ago, his high school coach called and said that Rob was interested in transferring.
"Rob will be a nice addition to our team. It's impossible to predict how it will end up," Miles continued. "Coming out of high school, he was very, very talented. Right now, he can't call a play for us. He has a long way to go."
Bolden, a 6-foot-3 native of Orchard Lake, Mich., completed 165 of 328 passes for 2,045 yards with seven touchdowns and 14 interceptions in his two seasons at Penn State.
Information from The Associated Press was used in this report.