This post has been updated.
A Web site for a super PAC with the same name also launched Tuesday.
The name of the PACs reflects the developing theme of Bush's possible campaign. An admirer of the late New York Republican Jack Kemp, whose politics revolved around poverty issues, Bush is hoping to cast himself as a new kind of Republican, in the Kemp mold, by touting his ideas on economic empowerment. (Rep. Paul Ryan, the GOP's 2012 vice-presidential nominee, has frequently used the phrase "right to rise" in speeches, as Bush has noted.)
Speaking at the Jack Kemp Foundation's awards dinner in 2013, Bush said, "We are a center right country but conservatives won’t govern again soon unless we adopt the Kemp example to get outside our comfort zones, and to listen, learn and persuade."
He added, "If he was with us now, I think he would agree we have strayed from the politics of winning, from the policies of opportunity and from achieving the governing needed to accomplish big things."
Bush made the announcement about the PAC in a Facebook post Tuesday.
He will visit Greenwich, Conn., on Wednesday to raise funds for it, one of many events he has held in recent weeks as he has ramped up his activity.
Greenwich was the hometown of the late Connecticut GOP senator Prescott Bush, Bush's grandfather, and has long been a place where the Bush family has deep roots. More fundraising trips are in the works, including stops in Washington and New York.
Bush said in December, in a Facebook statement, that he will "actively explore the possibility" of a run for the 2016 Republican presidential nomination.
Since beginning to consider a White House bid, Bush has resigned all of his corporate and nonprofit board memberships, including with his own education foundation. Touting his transparency, he has promised to release thousands of e-mails from his time as governor of Florida, where he served from 1999 to 2007. The e-mails are public record under Florida law, and The Post obtained many of them last month through a request filed with the state.
A Web site for Bush's PAC was also unveiled Tuesday, featuring smiling pictures of Americans of various ethnic backgrounds and a logo of a blue-colored right hand reaching for a blue star. Versions of the Web site were offered in English and Spanish. Bush is a fluent Spanish speaker.
Bush's PAC reflects a broader trend in the GOP to revamp the party's image and broaden its appeal, especially to the poor and middle-class voters.
Ryan (R-Wis.) has visited urban areas to meet with community and faith leaders. Sen. Marco Rubio (R-Fla.) has proposed changes to federal programs to help people climb out of poverty. And Sen. Rand Paul (R-Ky.) has revived Kemp's push for "economic freedom zones" in recession-plagued areas. All are potential 2016 presidential candidates.
In a video posted on the social-media site Instagram, Bush, walking casually in a dark winter jacket on a city street, said, "Hey, everybody, today we're setting up the Right to Rise PAC, which is a PAC to support candidates that believe in conservative principles to allow all Americans to rise up."
Not every commenter on the video was impressed. "What an awkwardly staged video: not looking that 'hip' to this Millennial voter, Jeb!" wrote one person.
Matea Gold contributed to this story.