"I will take nothing and no one for granted," the 62-year-old Bush, a son and brother of two ex-presidents, told a crowd of supporters at a university in Miami. "I will run with heart. I will run to win."
Bush jumped headlong into the presidential race Monday, insisting "America deserves better" after eight years of Barack Obama, as the Republican seeks to win over votes skeptical of his political pedigree.
Following a lengthy exploration of a White House bid, Bush made his formal announcement at Miami Dade College, a diverse university chosen to signal that he aims to run an inclusive 2016 campaign.
"I have decided. I am a candidate for president of the United States," he said. As the crowd roared, a relieved Bush uttered: "Whooo!"
While he is the son and brother of two former presidents, Bush highlighted his own political vision and his two terms as governor of Florida.
"We made Florida number one in job creation and number one in small business creation," Bush said, boasting that he slashed taxes by $19 billion.
"I know we can fix this. Because I've done it."
Bush also stressed he would campaign everywhere and face the issues, rather than rely on his record and family name.
"I will take nothing and no one for granted. I will run with heart. I will run to win," he said.
He also stressed that as president he would take Washington "out of the business of causing problems."
The phrasing marked a jab at the four US senators in the race -- Ted Cruz, Rand Paul, Lindsey Graham and fellow Florida conservative Marco Rubio -- and suggested Americans should seek an outsider with executive experience.
Bush, 62, has been running a de facto campaign for six months, raising millions of dollars and increasing his international profile with a trip last week to Europe.
Following his speech in Miami, he will set about trying to prove that, although he comes from the Bush political dynasty, he is his own man.
While he highlighted his own record, he knocked the Obama adminstration for what he called the "phone-it-in foreign policy, the Obama-Clinton-Kerry team (that) is leaving a legacy of crises uncontained, violence unopposed, enemies unnamed, friends undefended, and alliances unravelling."
"You and I know that America deserves better," he said.
Hillary Clinton is the frontrunner on the Democratic side, with no current close competition.
Nationally, Bush is bunched at the top of most Republican polls, but he is not the dominant figure many had expected.
He finished a dispiriting seventh last month in an Iowa poll, but dismisses his struggles to break free of the pack.
"People make up their mind in the last weeks of these primaries. So my expectation is that we'll have slow, steady progress," Bush told CNN.
He waded into a quagmire last month when he repeatedly stumbled over whether he would have authorized an invasion of Iraq.
The hiccups highlighted what will likely be one of the candidate's main challenges: overcoming the legacy of his brother George W. Bush, his unpopular Iraq policy and a second term that ended economic turmoil.
"We've already seen what a Bush economy looks like," Democratic National Committee chair Debbie Wasserman Schultz said Monday.
"Jeb would double down."
Some voters are less critical of his pedigree.
"To me the last name brings a lot of respect," Carlos Musivay, an entrepreneur who arrived early at Bush's Miami event, told AFP.
"It also brings the challenges of his brother, but we have to look at Jeb for Jeb," he added. "He's his own person. When he was governor it wasn't George W running Florida."
Grassroots conservatives have expressed skepticism, saying Bush has not put forward a compelling message since leaving the governorship eight years ago.
His support for comprehensive immigration reform places him to the left of virtually all Republican candidates on the issue, and his backing of national education standards is loathed by the far-right.
With many conservative primary voters demanding ideological purity, Bush has a tricky path to the nomination.
He needs to fend off younger, uncompromising conservatives that he acknowledged Monday are "good people" battling for the White House.
"It's nobody's turn," he said. "It's everybody's test -- and it's wide open."
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