MIAMI — Senator Marco Rubio of Florida announced on Monday that he is running for president, declaring that he is the best person to lead the United States into “another American century.”

Mr. Rubio made his announcement Monday evening during a speech here in which he presented himself as the embodiment of generational change who can unite the Republican Party’s factions and offer economic solutions for the 21st century.

At 43, the youngest candidate in the rapidly growing 2016 presidential field, Mr. Rubio cast himself as a forward-looking, next-generation leader — and an implicit contrast to Jeb Bush, 62, whose family has dominated Republican politics for nearly three decades, and Hillary Rodham Clinton, 67, the wife of a former president and the most likely Democratic nominee.

“Too many of our leaders and our ideas are stuck in the 20th century,” Mr. Rubio said, pointing to education and spending programs put in place by Democrats in the 1990s.

In a direct attack on Mrs. Clinton’s candidacy, which she announced Sunday, Mr. Rubio said: “Just yesterday, a leader from yesterday began a campaign for president by promising to take us back to yesterday. Yesterday is over and we’re never going back.”

And hinting at Mr. Bush’s background as the son and brother of presidents, Mr. Rubio said: “I live in an exceptional country where the son of a bartender and a maid can have the same dreams and the same future as those who come from power and privilege.”

Mr. Rubio ‘s speech also leaned heavily on the importance of keeping America safe in a dangerous world. Laying out what he considered foreign policy errors by President Obama, he lamented “dangerous concessions” to Iran and the administration’s “hostility” to Israel.

But ultimately Mr. Rubio made the argument that he was best suited to make the American dream that his family experienced accessible to others.

“This election is a generational choice about what kind of country we will be,” he said.

At a breakfast for bundlers of donations to his campaign on Monday at the Miami Marriott Biscayne Bay,Mr. Rubio pointed to the venue for his announcement Monday night — Miami’s Freedom Tower, which served as a processing center for thousands of Cuban refugees fleeing the government of Fidel Castro — as a sign of America’s greatness because the child of refugees children could run for president, an attendee said.

Mr. Rubio joins his Senate colleagues Ted Cruz of Texas and Rand Paul of Kentucky, who have announced their candidacies. Other Republican hopefuls, including Mr. Bush and Gov. Scott Walker of Wisconsin, are also preparing to officially enter the race.

Mrs. Clinton was on a road trip to Iowa after announcing her second bid for the Democratic nomination.

Mr. Rubio is expected to campaign on themes that emphasize American greatness and the American dream, an optimistic, aspirational message that he outlined in his newly released book, “American Dreams.”

He is also angling to become the youthful face of a party that skews older and has struggled to attract young voters, blacks and Latinos. Many mainstream Republicans hope that a Cuban-American who speaks fluent Spanish can help draw Hispanic voters, a growing demographic that will be critical during the general election, into the party.

Mr. Rubio served in the Florida House of Representatives from 2000 to 2008, eventually becoming speaker. He was elected to the United States Senate in 2010 and has said he would not run for re-election if he ran for president.

Among the Republican Party’s announced and expected candidates, Mr. Rubio occupies a middle ground, which is both an asset and an obstacle. He hopes to appeal to more moderate Republicans as well as to social, fiscal and foreign policy voters, but he could also find himself without a clear constituency, especially in the first four nominating states.

Mr. Rubio has credibility with the conservative grass roots after defeating both a Democrat and Charlie Crist, a former moderate Republican governor, in his Senate race, but he offers a message that is not as hard-line as those of Republicans like Mr. Cruz and Mr. Walker.

As a member of the Foreign Relations and Intelligence Committees, Mr. Rubio has used his time in the Senate to position himself as a hawk, a stark contrast with Mr. Paul, who prefers a more restrained approach to military intervention. After his announcement here, Mr. Rubio plans to travel back to Washington to attend a Foreign Relations committee meeting on legislation that would require Congress to weigh in on any nuclear deal reached with Iran.

But his work on immigration — one of his biggest achievements in the Senate — illustrates the delicate balance Mr. Rubio will have to strike to make it through his party’s nominating process. In 2013, Mr. Rubio was part of a bipartisan group of senators that drafted a broad immigration bill that included a pathway to citizenship for the 11 million unauthorized immigrants already in the country.

He has since distanced himself from the proposal, saying he believes any immigration overhaul must start with securing the nation’s southern border and proceed step by step. But his original legislation enraged the right, which saw it as amnesty, while many liberals and immigration groups thought he had not gone far enough and were frustrated with his position.

By making his announcement in Florida, the state that Mr. Bush governed for eight years, Mr. Rubio signaled that he planned to cede nothing to Mr. Bush, his former mentor.

In the weeks leading up to his announcement, Mr. Rubio concentrated on fund-raising and putting together a campaign team that aims to be seasoned but lean.

On Monday, he gathered some 60 bundlers of campaign donations, from all over the country, for the breakfast; the group was scheduled to have a lunch with Mr. Rubio’s campaign team and then get to work en masse for an afternoon round of fund-raising calls.

Raising money could be a challenge for Mr. Rubio, especially in light of Mr. Bush’s aggressive efforts and the large network of Bush family allies. And, because he is less known than some of his rivals, he will need to introduce himself to as many voters as possible, particularly in the early nominating states — Iowa, New Hampshire, South Carolina and Nevada.

On Friday, Mr. Rubio plans to do just that, heading to New Hampshire for a day of meetings with activists, business leaders and students, as well as the local news media. Friday evening, he will kick off the state party’s two-day leadership summit of 2016 hopefuls, speaking at a dinner in Nashua, N.H.