In a video released hours ahead of his official launch in Miami, the 62-year-old brother of ex-president George W Bush declared: “I’m ready to lead.”
He also promised to protect the country’s most vulnerable and remove the barriers to social mobility.
But doubts persist among conservatives in his party.
And early polling suggests that he has yet to dominate a wide field of Republican candidates.
In his latest video, entitled The Greatest Century, he strikes a very optimistic note, saying: “I see a great country on the verge of its greatest century, and I’m ready to lead.”
Analysis – Anthony Zurcher, BBC News, Washington
The Bush team may have hoped their man would have built a clear lead in the polls by now, but the consensus view is he’s currently just one in a pack of frontrunners.
Recent interviews with campaign strategists indicate that they are going to start using the millions of dollars at their disposal to target opponents they consider most threatening – namely, Wisconsin Governor Scott Walker and Florida Senator Marco Rubio.
In his opening campaign video, Mr Bush emphasised his positive, optimistic vision for the future, saying some politicians “talk about problems; I see solutions”.
But in the coming months, the fight for the Republican presidential nomination could get nasty.
Although his campaign becomes official on Monday, it’s been no secret for many months and his team is well on the way to raising a $100m war chest.
During a tour of Europe last week, Mr Bush warned he would not waver from his core beliefs, even if some are unpopular in his party.
“I’m not going to change who I am,” he said. “I respect people who may not agree with me, but I’m not going to change my views because today someone has a view that’s different.”
In a separate video, called Making A Difference, he champions the rights of women, ethnic minorities and the disabled.
“My core beliefs start with the premise that the most vulnerable in our society should be in the front of the line and not the back,” he says.
“What we need is new leadership that takes conservative principles and applies them so that people can rise up.”
John Ellis Bush
• known as “Jeb”
• second son of former US President George HW Bush
• met wife Columba in Mexico when a teenager
• worked in Caracas, Venezuela in the late 1970s
• has three children
• attended the University of Texas at Austin
• governor of Florida from 1999-2007
Profile: Jeb Bush
A Spanish language video was also released, demonstrating his strong Hispanic links – his wife Columba is Mexican and he speaks good Spanish.
But in recent weeks he has found himself on the defensive over the Iraq War – led by his older brother, President George W Bush – as he stumbled to clarify his position.
The issue brought into focus the problems he may face over his famous surname and the baggage that comes with it.
He becomes the 11th Republican to declare, with Wisconsin Governor Scott Walker and Florida Senator Marco Rubio among his biggest rivals.
On the Democratic side, Hillary Clinton is the clear frontrunner. This raises the possibility in 2016 of another Clinton-Bush race like that of 1992, when Mrs Clinton’s husband Bill beat Jeb Bush’s father, President George HW Bush.
• Hillary Clinton, former First Lady and Secretary of State
• Martin O’Malley, former governor of Maryland and mayor of Baltimore
• Bernie Sanders, independent senator from Vermont, caucuses with the Democrats
• Lincoln Chafee, former senator and governor of Rhode Island
• Jeb Bush, former Florida Governor
• Ted Cruz, Texas senator and conservative firebrand
• Rick Santorum, Christian conservative from Pennsylvania
• Marco Rubio, Florida senator since 2011
• George Pataki, former three-term governor of New York
• Ben Carson, author and neurosurgeon
• Carly Fiorina, former boss of Hewlett Packard
• Mike Huckabee, former governor of Arkansas
• Rand Paul, libertarian conservative Kentucky senator
• Lindsey Graham, South Carolina senator since 2003
• Rick Perry, former Texas governor