Booker, a Democrat, made the announcement during an event in Newark, The (Newark) Star-Ledger reported.
"It's official. I'm running for Senate. Please join my campaign today: https://cards.twitter.com/cards/9eu4d/6a #Booker4Senate," Booker tweeted Saturday.
Reps. Frank Pallone and Rush Holt said Friday they are seeking the Democratic nomination in the special election to replace Lautenberg, The New York Times reported.
Lautenberg's family released a statement Monday supporting Pallone's candidacy, calling him a "workhorse, not a showhorse."
"Frank Pallone, like Frank Lautenberg, has always looked out for working families in New Jersey and made them his top priority -- in fighting for economic justice, healthcare reform, environmental protection, education and so many other issues," ABC News quoted a letter written by the family as saying. "Frank Pallone, like our Frank, will put in the hours and hard work necessary to fight for New Jersey in the Senate. And Frank Pallone knows that gimmicks and celebrity status won't get you very far in the real battles that Democrats face in the future."
If he wins the nomination and the Oct. 16 election, Booker would be the first African-American to win a statewide office in New Jersey.
The only Republican candidate so far is Steve Lonegan, the former mayor of Bogota, a small suburb in northern New Jersey, the Times reported. Lonegan, a conservative who serves as state director of Americans for Prosperity, has run unsuccessfully twice for the Republican gubernatorial nomination, and once for Congress.
Pallone, who has been in Congress since 1994 representing a central New Jersey district, has a bigger war chest than Booker or Holt. Holt, a physicist whose supporters sport bumper stickers reading "My congressman IS a rocket scientist," is popular in his Princeton-area district but little-known in the rest of the state.
New Jersey's Republican governor, Chris Christie, scheduled a special election for October, three weeks before the state's off-year gubernatorial election. Critics suggested Christie feared being on the same ballot as Booker.
The primary is scheduled for Aug. 13, and candidates must declare by Monday.
Political analysts say the race is hard to call because of the timing.
"There's nothing we can go on that can help us predict who's going to show up and vote," Patrick Murray, a pollster at Monmouth University, told the Times.