As president, Bush said, he would set a goal of 4 percent economic growth and 19 million new jobs.
Bush's speech also addressed what he called a "phone-it-in foreign policy" from President Barack Obama and former Secretary of State Hillary Clinton. In addition to the administration's treatment of the military, Bush called out its attempts at normalizing relations with Cuba.
"We don't need a glorified tourist to go to Havana in support of a failed Cuba. We need an American president to go to Havana in solidarity with a free Cuban people, and I am ready to be that president," he said.
Iraq will be one of the issues Jeb looks to distance himself from, as he has before stressed that he is different from his older brother, George W. Bush. But winning the nomination will mean winning over Republican voters who might have preconceived notions stemming from his brother's or George H.W. Bush's prior presidencies.
Read More$100 million? Jeb Bush's high expectations problem
The Republican hopeful addressed the issue of his last name during his Monday speech.
"I know that there are good people running for president. Quite a few, in fact. And not a one of us deserves the job by right of resume, party, seniority, family, or family narrative," he said. "It's nobody's turn. It's everybody's test, and it's wide open—exactly as a contest for president should be."
One competitor, Florida Senator Marco Rubio, was among the first to extend a welcome to Bush ahead of his official entrance into the Republican field.
"In politics, people throw around the word 'friend' so much it often has little real meaning. This is not one of those times. When I call Jeb Bush my friend, I mean he is someone I like, care for and respect," Rubio said in a statement. "He is a passionate advocate for what he believes, and I welcome him to the race."
Bush had been the front runner for Republican voters when he floated the idea of a presidential bid, but as others have announced their own candidacy Bush's advantage in the polls has slowly dwindled. His muddled response to a question about the Iraq war didn't help things either, as Jeb now finds himself tied with a handful of other candidates.
—Reuters and CNBC's Zack Guzman contributed to this report.