The 13 inductees to the hall's second class also include funnymen Bud Abbott and Lou Costello, astronomer Carl Sagan, Yankee shortstop Phil Rizzuto and novelist F. Scott Fitzgerald. Actor Jack Nicolson, U.S. President Woodrow Wilson, musician Count Basie and novelist Philip Roth failed to make the grade.
A copy of the press release announcing the inductees was obtained in advance by The Associated Press.
"This group of hall of famers embodies the spirit of New Jersey, a combination of drive, determination and creativity that has led them to greatness," Gov. Jon Corzine said in a statement before introducing the class at a Monday morning news conference.
The winners were chosen by New Jerseyans, who had months to pick their favorites online, and the hall's Voting Academy, made up of 100 state organizations. The nominees came from the fields of sports, entertainment, science and the arts. All have deep ties to the Garden State.
Shaq is from Newark. Bon Jovi, born in Sayreville who now lives at the Shore, is building affordable housing in Newark and other cities through his charitable foundation. Robeson, a celebrated scholar, athlete and performer, was among the first African-American students at Rutgers University.
The goal of the hall is to highlight positive contributions in an oft-derided state renowned for corrupt politicians, belching refineries and stereotypical gangsters.
As Corzine said, "The New Jersey hall should serve as a reminder that the people of New Jersey strive for excellence and engage in myriad productive and rewarding activities that help society and give back to mankind."
Asked about his induction to the hall, O'Neal, now of the Phoenix Suns, called the award a "great and humbling honor.
"I hope that through this wonderful museum, my accomplishments both in the NBA and in the classroom can be an inspiration to others."
For Bon Jovi, the award could be especially sweet. Despite having sold millions of records in a career spanning more than 25 years, he was snubbed by the Rock 'n' Roll Hall of Fame by failing to gain a nomination last year, his first year of eligibility.
The induction ceremony will be in May at the New Jersey Performing Arts Center in Newark.
The Hall of Fame's inaugural class inducted in May included entertainers Frank Sinatra and Bruce Springsteen, inventor Albert Einstein, novelist Toni Morrison and baseball legend Yogi Berra.
The hall has a virtual home but no permanent physical location.
Plans are in the works for two satellite museums and a mobile museum that will travel around the state.
The hall is supported by private funds but operated by the New Jersey Sports and Exposition Authority.