Claiborne said he received a first-round grade, and many analysts feel he could be drafted with one of the first 10 picks.
"I'm sad about leaving but you only get this opportunity once in a lifetime," Claiborne said.
Brockers, a draft-eligible sophomore thanks to a redshirt season, said he has heard mixed reviews on which round he could land in.
"You hear first (round), and you hear the beginning of the second (round)," Brockers said. "I don't know where it's locked in at."
LSU coach Les Miles, who sat between both players on the stage, said he was in full support of both of their decisions.
"They both have had real consistent growth," Miles said. "And both been have been humble in their approach to learn football."
Shortly after the announcement, TigerSportDigest.com broke the news that junior wide receiver Rueben Randle will also enter the NFL Draft.
A source close to Randle said the decision was made during a family dinner in Bastrop, La., on Wednesday night, and the papers were sent off on Thursday afternoon.
Stick with TigerSportsDigest.com for more on these breaking stories.