“We have changed a city, despite the cynicism of so many who believed that real change here in Newark was impossible,” Mr. Booker said. “This is the truth of Newark, and I tell you right now that there is another city in America that needs some change. Too many have come to believe that Washington, D.C., is a place where nothing can get done, where people don’t work together, don’t compromise, don’t make progress. People don’t believe that Washington is a place that is sticking up for American families. This has to end.”

Mr. Booker, 44, had announced in December that he would run for Senate, but he anticipated running next year, when Senator Frank R. Lautenberg had said he would retire. After Senator Lautenberg’s death on Monday, Gov. Chris Christie declared the seat would be filled in a special election in mid-October with a primary little more than two months away.

Mr. Booker enters the race heavily favored: polls earlier in the year showed that he enjoyed far broader name recognition than any of his primary opponents.

But the special election will bring Mr. Booker greater competition than he might have otherwise faced: two of the state’s Democratic congressmen who had been reluctant to give up their seats to run next year have chosen to run now. Representative Rush D. Holt Jr. declared his candidacy last week, and aides to Representative Frank Pallone Jr. said he intended to declare in the next few days. Aides to Sheila Y. Oliver, the speaker of the State Assembly, said she was also exploring a run. Candidates must gather 1,000 signatures by Monday afternoon to formally enter the race.