Claiborne made his decision public in an announcement Thursday afternoon with coach Les Miles at LSU, while Shepard indicated on Twitter that he will not return for his senior season.
"My decision had nothing to do with the game on Monday and how the season ended," Claiborne, a junior, said Thursday afternoon in a joint announcement with Brockers and coach Les Miles. "I knew this day was going to come."
Wide receiver Rueben Randle is also entering the NFL draft, a source told ESPN's Joe Schad Thursday night. Randle led LSU with 53 catches for 917 yards and 10 touchdowns.
"I just felt like it was the right thing for me and my family," Randle told Schad.
Claiborne, the third-rated player on ESPN Scouts Inc.'s draft board, led LSU with six interceptions this season and returned one for a touchdown. The winner of the Jim Thorpe Award as the nation's top defensive back also was LSU's top kickoff returner, averaging 25 yards per return, with one touchdown that went 99 yards.
Claiborne, who is from Shreveport, initially came to LSU expecting to play wide receiver but was quickly converted to defensive back and played in seven games in a reserve role as a true freshman.
He started 12 games as a sophomore opposite 2010 Thorpe Award winner and current Arizona Cardinal Patrick Peterson. With teams often avoiding throwing to Peterson's side of the field, Claiborne saw a lot of balls come his way and responded with a team-leading five interceptions and also recovered a fumble.
This season, he was part of a defensive backfield that included fellow All-American Tyrann Mathieu. Claiborne's 11 career interceptions places him in a tie with several other players for sixth all-time at LSU.
Brockers' 54 tackles were seventh on LSU's defense. The redshirt sophomore was credited with 10 tackles for losses, including two sacks. He also had a forced fumble and intercepted a screen pass.
Their departures means the Tigers will have to replace two of their top defenders as they work to bounce back from Monday night's loss to Alabama in the BCS title game.
"After the game Monday, I thought about how it ended. I talked to my mom, my grandmother and people close to me," Brockers said. "I made a decision. I think it was a good decision."
Miles said he felt differently about the decisions of each player to turn pro, "but supported both."
"Mo is a top ten player, maybe a top-five player. There was no way for him to improve his draft status," Miles explained. "Michael could have improved his draft position (by staying at LSU). He made a family decision to fulfill an obligation to his family. They both did what they were asked to do for the program. What they leave is a legacy on how to do it."
Meanwhile, there had been some confusion about whether Shepard would be declaring for the draft or transferring from LSU, but a Tigers teammate told Schad that Shepard informed him of his intention to make himself eligible for the draft.
"Thanks for your support Tiger Nation...but I have to do what's best for my family and myself...Geaux Tigers," read Shepard's Twitter account.
The 6-foot-1 Shepard was a highly recruited quarterback/receiver who never fulfilled his potential in Baton Rouge.
After beginning the season under suspension for breaking an NCAA rule -- he discussed with a teammate an ongoing investigation concerning the relationship scouting service provider Willie Lyles had with LSU and other schools -- Shepard had only 14 catches for 190 yards and four touchdowns.
Shepard's career numbers in three seasons are 52 catches for 478 yards and five scores. He also rushed for two touchdowns as a sophomore.
Information from ESPN college football reporter Joe Schad and The Associated Press was included in this report.