"I think this country's at a generational moment where it needs to decide not what party it wants in charge but what kind of country are we going to want to be moving forward," Rubio told Stephanopoulos in an interview at the Florida senator's home. "I think the 21st century can be the American century, and I believe that I can lead this country in that direction. I can help lead it there from the Senate. I can lead it there as president."
When asked if Rubio believed he is the most qualified candidate to be president, he said: "I absolutely feel that way."
"We've reached a moment now, not just in my career, but the history of our country, where I believe that it needs a Republican Party that is new and vibrant, that understands the future, has an agenda for that future," Rubio said, "and I feel uniquely qualified to offer that. And that's why I'm running for president."
A few hours later, Rubio formally announced his campaign at the Freedom Tower, a downtown Miami building with historical significance for thousands of Cuban-Americans.
"Just yesterday, a leader from yesterday began a campaign for president by promising to take us back to yesterday," Rubio said to loud booing from the crowd. "But yesterday is over, and we are never going back."
While Rubio was referencing Clinton, his statements also applied to his former mentor Jeb Bush, who hails from a political dynasty.
"I have heard some suggest that I should step aside and wait my turn. But I cannot," he said. "Because I believe our very identity as an exceptional nation is at stake, and I can make a difference as president."
If he is elected president in 2016, Rubio would be the first Cuban-American to win the White House.
Rubio, 43, is the fourth major candidate to declare a run for the presidency this year. His announcement comes one day after Clinton announced her presidential bid.
Rubio was elected to the Senate in 2010 and lives in Miami with his wife Jeanette and four children.
Watch "World News Tonight With David Muir" and "Good Morning America" for more from ABC News Chief Anchor and "This Week" host George Stephanopoulos' exclusive interview with Senator Marco Rubio.